Deck 13: Temperature and the Ideal Gas

Question 1

If the temperature changes by $36^{\circ} \mathrm{F}$ , then what is the change in temperature in Celsius?

A) $26^{\circ} \mathrm{C}$
B) $40^{\circ} \mathrm{C}$
C) $15^{\circ} \mathrm{C}$
D) $32^{\circ} \mathrm{C}$
E) $20^{\circ} \mathrm{C}$

Answer 1

$20^{\circ} \mathrm{C}$

Question 2

If the temperature of a room is $62^{\circ} \mathrm{F}$ , then what is the temperature of the room in Kelvin?

A) $312.0 \mathrm{~K}$
B) $300.0 \mathrm{~K}$
C) $291.7 \mathrm{~K}$
D) $289.8 \mathrm{~K}$
E) $307.8 \mathrm{~K}$

Answer 2

$289.8 \mathrm{~K}$

Question 3

The temperature of a room is $300 \mathrm{~K}$ . What is the temperature in Fahrenheit?

A) $85.2^{\circ} \mathrm{F}$
B) $78.5^{\circ} \mathrm{F}$
C) $74.2^{\circ} \mathrm{F}$
D) $70.1^{\circ} \mathrm{F}$
E) $80.3^{\circ} \mathrm{F}$

Answer 3

$80.3^{\circ} \mathrm{F}$

Question 4

Abrass rod is $25.0 \mathrm{~cm}$ long at a temperature of $20.0^{\circ} \mathrm{C}$ . The coefficient of linear expansion of brass is $19.0 \times$ $10^{-6} /{ }^{\circ} \mathrm{C}$ . If the temperature changes to $25^{\circ} \mathrm{C}$ , then the increase in length of the brass rod is

A) $2.38 \times 10^{-5} \mathrm{~m}$ .
B) $3.03 \times 10^{-5} \mathrm{~m}$ .
C) $4.01 \times 10^{-5} \mathrm{~m}$ .
D) $1.65 \times 10^{-5} \mathrm{~m}$ .
E) $3.72 \times 10^{-5} \mathrm{~m}$ .

Question 5

An aluminum rod is $20.0 \mathrm{~cm}$ in length, has a diameter of $10.0 \mathrm{~mm}$ and is at a temperature of $20^{\circ} \mathrm{C}$ . The coefficient of linear expansion of aluminum is $23.0 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ . If the temperature changes to $50^{\circ} \mathrm{C}$ , then the increase in diameter of the aluminum rod is

A) $5.6 \times 10^{-3} \mathrm{~mm}$
B) $6.0 \times 10^{-3} \mathrm{~mm}$ .
C) $4.9 \times 10^{-3} \mathrm{~mm}$
D) $4.0 \times 10^{-3} \mathrm{~mm}$ .
E) $6.9 \times 10^{-3} \mathrm{~mm}$

Question 6

A $3.00 \mathrm{~cm} \times 5.00 \mathrm{~cm}$ rectangular piece of copper is at a temperature of $10.0^{\circ} \mathrm{C}$ . The coefficient of linearexpansion of copper is $17.0 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ . If the temperature of the copper rectangle increases by $2.00^{\circ} \mathrm{C}$ , thenwhat is its change in area?

A) $1.02 \times 10^{-3} \mathrm{~cm}^{2}$
B) $0.550 \times 10^{-3} \mathrm{~cm}^{2}$
C) $2.44 \times 10^{-3} \mathrm{~cm}^{2}$
D) $1.95 \times 10^{-3} \mathrm{~cm}^{2}$
E) $0.830 \times 10^{-3} \mathrm{~cm}^{2}$

Question 7

A 40.0 liter gas tank is filled to the brim with gasoline when the temperature is $5.00^{\circ} \mathrm{C}$ . Gasoline has a coefficient of volume expansion of $950 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ . If the gas tank is moved into the sun of a hot summer day, the temperature of the gas tank is increased to $60.0^{\circ} \mathrm{C}$ . What is the volume of gasoline that overflows the tank (ignore the expansion of the gas tank)?

A) 1.55 liters
B) 3.11 liters
C) 2.67 liters
D) 2.09 liters
E) 3.95 liters

Question 8

A 10.0 liter water bottle is filled to the brim with water when the temperature is $5.00^{\circ} \mathrm{C}$ . The bottle is sealed after it is completely filled with water. Water has a coefficient of volume expansion of $207 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ and a bulk modulus of $2.20 \times 10^{9} \mathrm{~N} / \mathrm{m}^{2}$ . If the temperature of the water tank is increased to $30.0^{\circ} \mathrm{C}$ , what is the increase in pressure of the water (ignore the expansion of the bottle)?

A) $2.73 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
B) $1.75 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
C) $1.14 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
D) $2.01 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$
E) $1.01 \times 10^{7} \mathrm{~N} / \mathrm{m}^{2}$

Question 9

The temperature of a copper cube is increased by $35.0^{\circ} \mathrm{C}$ . The linear coefficient of thermal expansion is 17.0 $\times 10^{-6} /{ }^{\circ} \mathrm{C}$ . The fractional change in volume is

A) $2.67 \times 10^{-3}$ .
B) $1.79 \times 10^{-3}$ .
C) $2.33 \times 10^{-3}$ .
D) $2.00 \times 10^{-3}$ .
E) $3.00 \times 10^{-3}$ .

Question 10

A copper plate has a hole with a diameter of $2.50 \mathrm{~cm}$ . A copper shaft with a diameter of $2.501 \mathrm{~cm}$ is to be inserted into the hole. If the linear coefficient of thermal expansion for copper is $17.0 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ , then what decrease in temperature of the copper shaft is required for the shaft to just fit inside the hole?

A) $33.3^{\circ} \mathrm{C}$
B) $39.5^{\circ} \mathrm{C}$
C) $30.1^{\circ} \mathrm{C}$
D) $23.5^{\circ} \mathrm{C}$
E) $26.4^{\circ} \mathrm{C}$

Question 11

A brass plate measures $30.0 \mathrm{~cm}$ by $40.0 \mathrm{~cm}$ . The coefficient of linear thermal expansion is $19.0 \times 10^{-6 /{ }^{\circ} }\mathrm{C} \text {. }$ If the temperature of the plate is increased by $10.0 \mathrm{~K}$ , then what is the increase in the area of the plate?

A) $0.555 \%$
B) $0.404 \mathrm{~cm}^{2}$
C) $0.456 \mathrm{~cm}^{2}$
D) $0.502 \mathrm{~cm}^{2}$
E) $0.350 \mathrm{~cm}^{2}$

Question 12

One mole of carbon- 12 has a mass of 12.00 grams. What is the mass of a ${ }^{12} \mathrm{C}$ atom?

A) $3.000 \times 10^{-26} \mathrm{~kg}$
B) $1.244 \times 10^{-26} \mathrm{~kg}$
C) $2.440 \times 10^{-26} \mathrm{~kg}$
D) $1.993 \times 10^{-26} \mathrm{~kg}$
E) $2.032 \times 10^{-26} \mathrm{~kg}$

Question 13

A sample of water has a mass of 10.0 grams. What is the number of molecules of water in the sample? $(\mathrm{H}=$ $1 \mathrm{u}, \mathrm{O}=16 \mathrm{u}$ , and $1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{~kg}$ .)

A) $2.00 \times 10^{23}$
B) $3.35 \times 1023$
C) $4.25 \times 1023$
D) $1.99 \times 10^{23}$
E) $2.56 \times 10^{23}$

Question 14

A sample of $\mathrm{CO}_{2}$ has a mass of 50.0 grams. What is number of molecules of carbon dioxide in the sample? ( $\mathrm{C}=12.0 \mathrm{u}, \mathrm{O}=16.0 \mathrm{u}$ , and $1 \mathrm{u}=1.66 \times 10^{-27} \mathrm{~kg}$ .)

A) $6.85 \times 10^{23}$
B) $4.95 \times 1023$
C) $5.66 \times 1023$
D) $4.02 \times 1023$
E) $6.02 \times 10^{23}$

Question 15

An ideal gas is at a pressure of 2.0 atmospheres and a temperature of $35^{\circ} \mathrm{C}$ . What is the molar density?

A) $60 \mathrm{~mol} / \mathrm{m}^{3}$
B) $70 \mathrm{~mol} / \mathrm{m}^{3}$
C) $79 \mathrm{~mol} / \mathrm{m}^{3}$
D) $84 \mathrm{~mol} / \mathrm{m}^{3}$
E) $67 \mathrm{~mol} / \mathrm{m}^{3}$

Question 16

An ideal gas composed of helium atoms is at a pressure of 2.00 atmospheres and a temperature of $35.0^{\circ} \mathrm{C}$ . What is the mass density? $(\mathrm{He}=4.00 \mathrm{u})$

A) $0.276 \mathrm{~kg} / \mathrm{m}^{3}$
B) $0.534 \mathrm{~kg} / \mathrm{m}^{3}$
C) $0.488 \mathrm{~kg} / \mathrm{m}^{3}$
D) $0.316 \mathrm{~kg} / \mathrm{m}^{3}$
E) $0.400 \mathrm{~kg} / \mathrm{m}^{3}$

Question 17

An ideal gas composed of a mixture of oxygen and nitrogen is at a pressure of 1.50 atmospheres and a temperature of $25.0^{\circ} \mathrm{C}$ . What is the molar density?

A) $40.0 \mathrm{~mol} / \mathrm{m}^{3}$
B) $55.5 \mathrm{~mol} / \mathrm{m}^{3}$
C) $79.3 \mathrm{~mol} / \mathrm{m}^{3}$
D) $47.6 \mathrm{~mol} / \mathrm{m}^{3}$
E) $61.3 \mathrm{~mol} / \mathrm{m}^{3}$

Question 18

One mole of an ideal gas has a volume of $0.0224 \mathrm{~m}^{3}$ and a pressure of $101.3 \times 10^{3} \mathrm{~Pa}$ . What is the absolute temperature of the gas?

A) $352 \mathrm{~K}$
B) $346 \mathrm{~K}$
C) $273 \mathrm{~K}$
D) $376 \mathrm{~K}$
E) $325 \mathrm{~K}$

Question 19

A sample of an ideal gas has a volume of $0.0100 \mathrm{~m}^{3}$ , a pressure of $100 \times 10^{3} \mathrm{~Pa}$ , and a temperature of 300 $\mathrm{K}$ . What is the number of moles in the sample of gas?

A) 0.330
B) 0.502
C) 0.375
D) 0.302
E) 0.401

Question 20

A sample of an ideal gas has a volume of $0.00100 \mathrm{~m}^{3}$ , a pressure of 4.50 atmospheres and $2.00 \times 1023$ particles. What is the temperature of the gas?

A) $165 \mathrm{~K}$
B) $173 \mathrm{~K}$
C) $154 \mathrm{~K}$
D) $194 \mathrm{~K}$
E) $186 \mathrm{~K}$

Question 21

ideal gas has a pressure of $2.5 \mathrm{~atm}$ , a volume of $1.0 \mathrm{~L}$ at a temperature of $30^{\circ} \mathrm{C}$ . How many molecules are there in the gas?

A) $2.3 \times 1023$
B) $6.1 \times 1023$
C) $6.1 \times 1022$
D) $2.4 \times 10^{23}$

Question 22

An sample of helium occupies $44.8 \mathrm{~L}$ at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $\left.1 \mathrm{~atm}\right)$ . What is the mass of the sample? The atomic mass of helium is $4.00 \mathrm{u}$ .

A) $4.00 \mathrm{~g}$
B) $16.0 \mathrm{~g}$
C) $8.00 \mathrm{~g}$
D) $2.00 \mathrm{~g}$

Question 23

One mole of an ideal gas with a volume of 4.00 liters and a temperature of $0^{\circ} \mathrm{C}$ is mixed with one mole of an ideal gas with a volume of 2.00 liters and a temperature of $100^{\circ} \mathrm{C}$ . The volume of the mixture is 6 liters. What is the number density of the mixture?

A) $3.56 \times 10^{26} \mathrm{~m}^{-3}$
B) $2.66 \times 10^{26} \mathrm{~m}^{-3}$
C) $3.21 \times 10^{26} \mathrm{~m}^{-3}$
D) $1.75 \times 10^{26} \mathrm{~m}^{-3}$
E) $2.01 \times 10^{26} \mathrm{~m}^{-3}$

Question 24

Two moles of an ideal gas with a volume of 4.00 liters and a temperature of $0^{\circ} \mathrm{C}$ are mixed with one mole of an ideal gas with a volume of 3.00 liters and a temperature of $100^{\circ} \mathrm{C}$ . The volume of the mixture is 5.00 liters. What is the number density of the mixture?

A) $3.61 \times 10^{26} \mathrm{~m}^{-3}$
B) $1.98 \times 10^{26} \mathrm{~m}^{-3}$
C) $2.02 \times 10^{26} \mathrm{~m}^{-3}$
D) $4.00 \times 10^{26} \mathrm{~m}^{-3}$
E) $2.56 \times 10^{26} \mathrm{~m}^{-3}$

Question 25

An ideal gas is at a temperature of $30^{\circ} \mathrm{C}$ and a pressure of 2.00 atmospheres. What is the number of particles per unit volume of the gas?

A) $6.23 \times 10^{25} \mathrm{~m}^{-3}$
B) $5.98 \times 10^{25} \mathrm{~m}^{-3}$
C) $4.85 \times 10^{25} \mathrm{~m}^{-3}$
D) $5.15 \times 10^{25} \mathrm{~m}^{-3}$
E) $6.02 \times 10^{25} \mathrm{~m}^{-3}$

Question 26

An ideal gas is at a temperature of $60^{\circ} \mathrm{C}$ and a pressure of 1.50 atmospheres. What is the volume per particle of the gas?

A) $5.00 \times 10-26 \mathrm{~m}^{3}$
B) $3.98 \times 10-26 \mathrm{~m}^{3}$
C) $2.75 \times 10^{-26} \mathrm{~m}^{3}$
D) $3.02 \times 10^{-26} \mathrm{~m}^{3}$
E) $4.25 \times 10-26 \mathrm{~m}^{3}$

Question 27

An ideal gas is at a temperature of $40^{\circ} \mathrm{C}$ and a pressure of 2.00 atmospheres. If the diameter of an $\mathrm{N}_{2}$ molecule is $0.300 \mathrm{~nm}$ , then what is the mean free path of the $\mathrm{N}_{2}$ molecule in the gas?

A) $6.02 \times 10^{-8} \mathrm{~m}$
B) $5.33 \times 10^{-8} \mathrm{~m}$
C) $4.75 \times 10^{-8} \mathrm{~m}$
D) $5.00 \times 10^{-8} \mathrm{~m}$
E) $4.01 \times 10^{-8} \mathrm{~m}$

Question 28

What is the average distance between air molecules at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $\left.1 \mathrm{~atm}\right)$ ?

A) $2.07 \mathrm{~nm}$
B) $3.34 \mathrm{~nm}$
C) $0.00 \mathrm{~nm}$
D) $2.03 \mathrm{~nm}$

Question 29

At what approximate temperature would the rms speed of $\mathrm{H}_{2}$ molecules equal the Earth's escape speed $(11,200 \mathrm{~m} / \mathrm{s})$ ?

A) $10^{8} \mathrm{~K}$
B) $102 \mathrm{~K}$
C) $106 \mathrm{~K}$
D) $104 \mathrm{~K}$

Question 30

What is the average kinetic energy per particle in 1.00 mole of an ideal gas at a pressure of 1.50 atmospheres and a volume of 2.00 liters?

A) $8.24 \times 10-22 \mathrm{~J}$
B) $6.02 \times 10-22 \mathrm{~J}$
C) $6.67 \times 10-22 \mathrm{~J}$
D) $5.35 \times 10^{-22} \mathrm{~J}$
E) $7.57 \times 10-22 \mathrm{~J}$

Question 31

What is the average kinetic energy per particle in 1.00 mole of an ideal gas at a pressure of 1.50 atmospheres and a temperature of $20^{\circ} \mathrm{C}$ ?

A) $6.03 \times 10-21 \mathrm{~J}$
B) $5.05 \times 10-21 \mathrm{~J}$
C) $4.75 \times 10-21 \mathrm{~J}$
D) $6.67 \times 10^{-21} \mathrm{~J}$
E) $6.07 \times 10^{-21} \mathrm{~J}$

Question 32

The total kinetic energy in one mole of an ideal gas is $4,000 \mathrm{~J}$ . What is the average kinetic energy of an individual particle in the ideal gas?

A) $6.64 \times 10^{-21} \mathrm{~J}$
B) $4.86 \times 10^{-21} \mathrm{~J}$
C) $5.03 \times 10^{-21} \mathrm{~J}$
D) $4.04 \times 10^{-21} \mathrm{~J}$
E) $3.78 \times 10^{-21} \mathrm{~J}$

Question 33

A container of volume 2.00 liters contains 2.00 moles of an ideal gas at a pressure of 1.50 atmospheres. What is the average kinetic energy per particle in the gas?

A) $3.78 \times 10-22 \mathrm{~J}$
B) $3.96 \times 10-22 \mathrm{~J}$
C) $1.98 \times 10^{-22} \mathrm{~J}$
D) $2.83 \times 10-22 \mathrm{~J}$
E) $2.52 \times 10-22 \mathrm{~J}$

Question 34

If the root mean square velocity of the particles in a gas is $450 \mathrm{~m} / \mathrm{s}$ , and a particle collides with another particle every $2.0 \times 10^{-9}$ seconds on average, then the mean free path is

A) $9.0 \times 10^{-7} \mathrm{~m}$ .
B) $6.0 \times 10^{-7} \mathrm{~m}$ .
C) $6.9 \times 10^{-7} \mathrm{~m}$ .
D) $85 \times 10^{-7} \mathrm{~m}$ .
E) $7.5 \times 10^{-7} \mathrm{~m}$ .

Question 35

The mean free path of a molecule is $2.25 \times 10^{-7} \mathrm{~m}$ in an ideal gas at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $1 \mathrm{~atm})$ . What is the mean free path if the diameter of the molecule is doubled?

A) $0.56 \times 10^{-7} \mathrm{~m}$
B) $0.45 \times 10^{-7} \mathrm{~m}$
C) $0.75 \times 10^{-7} \mathrm{~m}$
D) $1.13 \times 10^{-7} \mathrm{~m}$
E) $0.23 \times 10^{-7} \mathrm{~m}$

Question 36

The mean free path of a molecule is $2.25 \times 10^{-7} \mathrm{~m}$ in an ideal gas at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $1 \mathrm{~atm}$ ). What is the mean free path if the diameter of the molecule and the temperature of the gas are both doubled?

A) $1.13 \times 10^{-7} \mathrm{~m}$
B) $2.25 \times 10^{-7} \mathrm{~m}$
C) $3.00 \times 10^{-7} \mathrm{~m}$
D) $3.75 \times 10^{-7} \mathrm{~m}$
E) $0.75 \times 10^{-7} \mathrm{~m}$

Question 37

The mean free path of a molecule is $2.25 \times 10^{-7} \mathrm{~m}$ in an ideal gas at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $1 \mathrm{~atm})$ . What is the mean free path if the pressure of the gas is doubled but the temperature is constant?

A) $2.25 \times 10^{-7} \mathrm{~m}$
B) $3.38 \times 10^{-7} \mathrm{~m}$
C) $1.13 \times 10^{-7} \mathrm{~m}$
D) $0.75 \times 10^{-7} \mathrm{~m}$
E) $3.75 \times 10^{-7} \mathrm{~m}$

Question 38

The mean free path of a molecule is $2.25 \times 10^{-7} \mathrm{~m}$ in an ideal gas at standard temperature and pressure $\left(0^{\circ} \mathrm{C}\right.$ and $1 \mathrm{~atm})$ . What is the mean free path if the pressure of the gas is doubled and the temperature is tripled?

A) $0.75 \times 10^{-7} \mathrm{~m}$
B) $3.38 \times 10^{-7} \mathrm{~m}$
C) $3.75 \times 10^{-7} \mathrm{~m}$
D) $2.25 \times 10^{-7} \mathrm{~m}$
E) $1.13 \times 10^{-7} \mathrm{~m}$

Question 39

The reaction rate of a chemical reaction doubles when the temperature increases from $10^{\circ} \mathrm{C}$ to $50^{\circ} \mathrm{C}$ . What is the activation energy?

A) $3.85 \times 10^{-20} \mathrm{~J}$
B) $2.19 \times 10^{-20} \mathrm{~J}$
C) $1.76 \times 10^{-20} \mathrm{~J}$
D) $2.98 \times 10^{-20} \mathrm{~J}$
E) $3.33 \times 10^{-20} \mathrm{~J}$

Question 40

What is the activation energy of a chemical reaction if the reaction rate triples when the temperature goes from $10^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$ ?

A) $6.0 \times 10^{-20} \mathrm{~J}$
B) $7.0 \times 10^{-20} \mathrm{~J}$
C) $6.5 \times 10^{-20} \mathrm{~J}$
D) $5.5 \times 10^{-20} \mathrm{~J}$
E) $7.5 \times 10^{-20} \mathrm{~J}$

Question 41

The diffusion constant for oxygen through water is $1.0 \times 10^{-9} \mathrm{~m}^{2} / \mathrm{s}$ . What is the time for an oxygen molecule to diffuse $1 \mathrm{~cm}$ ?

A) $5.0 \times 10^{4} \mathrm{sec}$
B) $6.0 \times 10^{4} \mathrm{sec}$
C) $2.0 \times 10^{4} \mathrm{sec}$
D) $4.0 \times 10^{4} \mathrm{sec}$
E) $3.0 \times 10^{4} \mathrm{sec}$

Question 42

The diffusion constant for oxygen diffusing through tissue is $1.0 \times 10^{-11} \mathrm{~m} 2 / \mathrm{s}$ . In a certain sample oxygen diffuses through the tissue at a rate of $2.0 \times 10^{-6} \mathrm{~kg} / \mathrm{s}$ . If the thickness of the tissue is doubled, then what is the rate of oxygen flow through the tissue?

A) $0.6 \times 10^{-6} \mathrm{~kg} / \mathrm{s}$
B) $0.4 \times 10^{-6} \mathrm{~kg} / \mathrm{s}$
C) $1.2 \times 10^{-6} \mathrm{~kg} / \mathrm{s}$
D) $1.0 \times 10^{-6} \mathrm{~kg} / \mathrm{s}$
E) $1.5 \times 10^{-6} \mathrm{~kg} / \mathrm{s}$

Question 43

What are the dimensions of the diffusion constant?

A) $\mathrm{m}^{2} / \mathrm{s}$
B) $\mathrm{m} / \mathrm{s}^{2}$
C) $\mathrm{m}^{3 / \mathrm{s}^{2}}$
D) $\mathrm{m} / \mathrm{s} 3$
E) $\mathrm{m}^{3 / \mathrm{s}}$

Question 44

The density of copper at $293 \mathrm{~K}$ is $8,940 \mathrm{~kg} / \mathrm{m}^{3}$ and its linear expansion coefficient is $17.0 \times 10^{-6} \mathrm{~K}^{-1}$ . Consider a hot cube of copper that is $1.0 \mathrm{~cm}$ on a side when its temperature is $1.356 \mathrm{~K}$ . What is the cube's mass?

A) $8.78 \mathrm{~g}$
B) $8.80 \mathrm{~g}$
C) $8.48 \mathrm{~g}$
D) $8.94 \mathrm{~g}$
E) $8.38 \mathrm{~g}$

Question 45

$147.5 \mathrm{ml}$ of ethyl alcohol (coefficient of volume expansion $\beta=1,120 \times 10^{-6} \mathrm{~K}^{-1}$ ), at a temperature of 273.1 $\mathrm{K}$ , is poured into a $150.0 \mathrm{ml}$ glass beaker (whose coefficient of volume expansion is negligible by comparison). To what temperature does the beaker have to be warmed for it to be completely full (i.e., for the volume of the alcohol to reach $150.0 \mathrm{ml})$ ?

A) $288.0 \mathrm{~K}$
B) $283.1 \mathrm{~K}$
C) $278.1 \mathrm{~K}$
D) $288.2 \mathrm{~K}$

Question 46

A $50.00 \mathrm{ml}$ sample of mercury at room temperature $(293.0 \mathrm{~K})$ is cooled. What is the volume of the sample when the mercury reaches $273.0 \mathrm{~K}$ ? The coefficient of volume expansion of mercury is $182.0 \times 10^{-6} \mathrm{~K}^{-1}$ .

A) $49.82 \mathrm{ml}$
B) $49.96 \mathrm{ml}$
C) $49.94 \mathrm{ml}$
D) $48.18 \mathrm{ml}$
E) $49.39 \mathrm{ml}$

Question 47

A glass thermometer using a thin column of ethyl alcohol at room temperature $(293.0 \mathrm{~K})$ is cooled. When the temperature reaches $273.0 \mathrm{~K}$ the column of alcohol is $15.50 \mathrm{~cm}$ high. How tall was it when the temperature was $293.0 \mathrm{~K}$ ? The coefficient of volume expansion of ethyl alcohol is $1,120 \times 10^{-6} \mathrm{~K}^{-1}$ .

A) $15.85 \mathrm{~cm}$
B) Cannot answer without knowing the diameter of the column
C) $15.68 \mathrm{~cm}$
D) $15.62 \mathrm{~cm}$

Question 48

What is the mass of exactly 1 million helium atoms? The atomic mass of helium is $4.00 \mathrm{u}$ .

A) $6.6 \times 10^{-21} \mathrm{~kg}$
B) $6.0 \times 10^{-17} \mathrm{~kg}$
C) $6.6 \times 10^{-18} \mathrm{~kg}$
D) $6.0 \times 10^{-20} \mathrm{~kg}$

Question 49

The mass of 6 million molecules of a diatomic gas is $5.1 \times 10-19 \mathrm{~kg}$ . What is the atomic mass of the element in this gas?

A) $5.10 \mathrm{u}$
B) $2.55 \mathrm{u}$
C) $25.6 \mathrm{u}$
D) $51.2 \mathrm{u}$

Question 50

The mass density of pure water is $1,000 \mathrm{~kg} / \mathrm{m}^{3}$ . If the molecular mass of water is $18.0 \mathrm{u}$ , how many water molecules are in spherical water balloon of radius $1.0 \mathrm{~cm}$ ?

A) $1.4 \times 10^{23}$
B) $1.0 \times10^{23}$
C) $2.5 \times 10^{24}$
D) $4.2 \times 10^{23}$

Question 51

The mass density of normal air at a certain temperature is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$ . If the average molecular mass of air is $29.0 \mathrm{u}$ , how many air molecules are in spherical balloon of radius $15.0 \mathrm{~cm}$ ?

A) $3.8 \times 10^{23}$
B) $2.5 \times 10^{25}$
C) $3.3 \times 10^{25}$
D) $8.5 \times 10^{23}$
E) $1.1 \times 10^{24}$
F) $9.8 \times 10^{24}$

Question 52

The mass density of normal air at room temperature (293 K) is $1.29 \mathrm{~kg} / \mathrm{m}^{3}$ , and the average molecular mass of air is $29.0 \mathrm{u}$ . If the mean free path of an air molecule at room temperature is measured to be $111 \mathrm{~nm}$ , what is the average diameter of an air molecule?

A) $0.31 \mathrm{~nm}$
B) $0.23 \mathrm{~nm}$
C) $0.49 \mathrm{~nm}$
D) $0.26 \mathrm{~nm}$
E) $0.28 \mathrm{~nm}$
F) $0.56 \mathrm{~nm}$

Question 53

A nitrogen molecule has a diameter of about $0.29 \mathrm{~nm}$ . The mean free path of a nitrogen molecule in a tank of dry nitrogen at room temperature $(293 \mathrm{~K})$ and standard pressure $(1 \mathrm{~atm})$ is about $0.10 \mu \mathrm{m}$ . A tank containing nitrogen at standard temperature $(273 \mathrm{~K})$ and pressure has volume $\mathrm{V}$ . If the tank is compressed by means of a piston to $20 \%$ of its original volume, what is the mean free path for a nitrogen molecule under the new conditions?

A) $0.125 \mu \mathrm{m}$
B) $0.112 \mu \mathrm{m}$
C) $0.020 \mu \mathrm{m}$
D) $0.080 \mu \mathrm{m}$

Question 54

The mean free path for a nitrogen molecule in a tank of dry nitrogen at $273 \mathrm{~K}$ is $0.15 \mu \mathrm{m}$ . If the diameter of a nitrogen molecule is $0.29 \mathrm{~nm}$ , what is the pressure in the tank?

A) $67.2 \mathrm{kPa}$
B) $211 \mathrm{kPa}$
C) $95.1 \mathrm{kPa}$
D) $48.0 \mathrm{kPa}$
E) $299 \mathrm{kPa}$

Question 55

A particular chemical reaction occurs at room temperature (293 K) at half the rate that it does at $300 \mathrm{~K}$ . What is the activation energy for this reaction?

A) $1.73 \times 10^{-19} \mathrm{~J}$
B) $1.17 \times 10^{-19} \mathrm{~J}$
C) $1.20 \times 10^{-19} \mathrm{~J}$
D) $1.69 \times 10^{-19} \mathrm{~J}$

Question 56

A particular chemical reaction that produces hydrogen gas as a byproduct has an activation energy of $19.2 \times$ $10^{-20} \mathrm{~J}$ . If the reaction produces $0.15 \times 10^{-3} \mathrm{~mol} \mathrm{H}_{2} / \mathrm{hr}$ at room temperature $\left(20^{\circ} \mathrm{C}\right)$ , what is the rate of production of $\mathrm{H}_{2}$ at $52^{\circ} \mathrm{C}$ ?

A) $0.24 \times 10^{-3} \mathrm{~mol} / \mathrm{hr}$
B) $0.14 \times 10^{-5} \mathrm{~mol} / \mathrm{hr}$
C) $0.16 \times 10^{-2} \mathrm{~mol} / \mathrm{hr}$
D) $0.14 \times 10^{-3} \mathrm{~mol} / \mathrm{hr}$