Units and Introduction to Gas Laws

Homework 1 Solutions have not been released yet.

Each question has only one correct answer. Use kelvin in gas-law calculations involving temperature. Keep units in intermediate calculations.

Part I - Easy Level (1-10)

Problem 1Easy

What is the SI base unit of temperature?

A. Celsius
B. Kelvin
C. Fahrenheit
D. Joule
E. Pascal

Problem 2Easy

How many milliliters are in $1\ \mathrm{L}$?

A. 10
B. 100
C. 1000
D. 10000
E. 0.001

Problem 3Easy

What is $25.0\,^{\circ}\mathrm{C}$ in kelvin?

A. 248.15 K
B. 273.15 K
C. 298.15 K
D. 300.15 K
E. 325.15 K

Problem 4Easy

How many kilopascals are in $1\ \mathrm{bar}$?

A. 1 kPa
B. 10 kPa
C. 100 kPa
D. 101.325 kPa
E. 1000 kPa

Problem 5Easy

How many $\mathrm{mmHg}$ are in $1\ \mathrm{atm}$?

A. 76
B. 100
C. 101.325
D. 760
E. 101325

Problem 6Easy

Which is the correct definition of pressure?

A. Mass per unit volume
B. Force per unit area
C. Distance traveled per unit time
D. Product of mass and volume
E. Product of force and area

Problem 7Easy

Which formula is used to calculate the amount of substance from mass?

A. $n=mM$
B. $n=M/m$
C. $n=m/M$
D. $n=N_{\mathrm A}/N$
E. $n=PV$

Problem 8Easy

Which four quantities directly describe the state of a gas?

A. $m$, $F$, $A$, $t$
B. $P$, $V$, $T$, $n$
C. $P$, $m$, $v$, $t$
D. $V$, $M$, $N$, $F$
E. $T$, $d$, $m$, $A$

Problem 9Easy

Which equation is the ideal gas law?

A. $P=F/A$
B. $n=m/M$
C. $PV=nRT$
D. $P_1V_1=P_2V_2$
E. $V=m/\rho$

Problem 10Easy

At constant temperature, what happens to the pressure of a gas if its volume decreases?

A. It decreases
B. It increases
C. It remains unchanged
D. It becomes zero
E. It first increases and then decreases

Part II - Medium Level (11-20)

Problem 11Medium

How many liters are in $2.50\ \mathrm{m^3}$?

A. 2.50 L
B. 25.0 L
C. 250 L
D. 2500 L
E. 25000 L

Problem 12Medium

What is $450\ \mathrm{mmHg}$ in atmospheres?

A. 0.450 atm
B. 0.592 atm
C. 0.760 atm
D. 1.69 atm
E. 3.42 atm

Problem 13Medium

What is $2.20\ \mathrm{bar}$ in kilopascals?

A. 22.0 kPa
B. 202 kPa
C. 220 kPa
D. 223 kPa
E. 2200 kPa

Problem 14Medium

What is $320.00\ \mathrm{K}$ in degrees Celsius?

A. $-46.85\,^{\circ}\mathrm{C}$
B. $32.00\,^{\circ}\mathrm{C}$
C. $46.85\,^{\circ}\mathrm{C}$
D. $593.15\,^{\circ}\mathrm{C}$
E. $320.00\,^{\circ}\mathrm{C}$

Problem 15Medium

How many moles are in $6.40\ \mathrm g$ of $\mathrm{O_2}$? $M(\mathrm{O_2})=32.0\ \mathrm{g\,mol^{-1}}$.

A. 0.100 mol
B. 0.200 mol
C. 0.500 mol
D. 5.00 mol
E. 205 mol

Problem 16Medium

What volume does $0.250\ \mathrm{mol}$ of an ideal gas occupy at $300\ \mathrm K$ and $1.00\ \mathrm{atm}$?

$R=0.08206\ \mathrm{L\,atm\,mol^{-1}\,K^{-1}}$

A. 2.05 L
B. 4.10 L
C. 6.15 L
D. 12.3 L
E. 24.6 L

Problem 17Medium

What is the amount of substance of a gas at $150\ \mathrm{kPa}$, $4.00\ \mathrm L$, and $300\ \mathrm K$?

$R=8.314\ \mathrm{L\,kPa\,mol^{-1}\,K^{-1}}$

A. 0.0802 mol
B. 0.120 mol
C. 0.241 mol
D. 0.500 mol
E. 1.66 mol

Problem 18Medium

A gas initially has a pressure of $120\ \mathrm{kPa}$ and a volume of $3.00\ \mathrm L$. At constant temperature, its volume decreases to $2.00\ \mathrm L$. What is the final pressure?

A. 80 kPa
B. 120 kPa
C. 160 kPa
D. 180 kPa
E. 240 kPa

Problem 19Medium

The pressure of a gas in a rigid closed container is $100\ \mathrm{kPa}$ at $300\ \mathrm K$. What will the pressure be if the temperature increases to $360\ \mathrm K$?

A. 83.3 kPa
B. 100 kPa
C. 120 kPa
D. 160 kPa
E. 360 kPa

Problem 20Medium

At constant pressure, a gas has a volume of $2.50\ \mathrm L$ at $250\ \mathrm K$. What will its volume be at $300\ \mathrm K$?

A. 2.08 L
B. 2.50 L
C. 3.00 L
D. 3.50 L
E. 5.00 L

Part III - Relatively Difficult Level (21-30)

Problem 21Hard

A gas initially has $P_1=100\ \mathrm{kPa}$, $V_1=2.00\ \mathrm L$, and $T_1=300\ \mathrm K$. In the final state, $V_2=1.50\ \mathrm L$ and $T_2=450\ \mathrm K$. What is $P_2$?

A. 50.0 kPa
B. 100 kPa
C. 150 kPa
D. 200 kPa
E. 300 kPa

Problem 22Hard

A gas has a volume of $500\ \mathrm{mL}$ at a pressure of $1.20\ \mathrm{atm}$. If the temperature remains constant and the volume changes to $0.300\ \mathrm L$, what is the final pressure?

A. 0.720 atm
B. 1.20 atm
C. 1.50 atm
D. 2.00 atm
E. 3.60 atm

Problem 23Hard

What volume does $8.80\ \mathrm g$ of $\mathrm{CO_2}$ occupy at $273.15\ \mathrm K$ and $1.00\ \mathrm{atm}$?

$M(\mathrm{CO_2})=44.0\ \mathrm{g\,mol^{-1}}$

A. 2.24 L
B. 4.48 L
C. 8.80 L
D. 11.2 L
E. 22.4 L

Problem 24Hard

A $0.500\ \mathrm{mol}$ sample of gas occupies $6.15\ \mathrm L$ at a pressure of $2.00\ \mathrm{atm}$. Approximately what is its temperature?

A. 150 K
B. 200 K
C. 250 K
D. 300 K
E. 600 K

Problem 25Hard

According to the expression $R=PV/(nT)$, what is the SI unit of $R$?

A. $\mathrm{Pa\,m^3\,mol^{-1}\,K^{-1}}$
B. $\mathrm{Pa\,m^{-3}\,mol\,K}$
C. $\mathrm{kg\,m^{-3}}$
D. $\mathrm{N\,m^{-2}}$
E. $\mathrm{L\,mol\,K^{-1}}$

Problem 26Hard

When comparing two states of the same closed gas sample using the combined gas law, why does $R$ not appear?

A. Because $R=0$
B. Because the temperature is constant
C. Because the same $nR$ term appears in both states and cancels
D. Because pressure is measured in atmospheres
E. Because volume is measured in liters

Problem 27Hard

A gas is compressed at constant temperature from $4.00\ \mathrm L$ to $1.00\ \mathrm L$. Its initial pressure is $80.0\ \mathrm{kPa}$. What is the final pressure?

A. 20.0 kPa
B. 80.0 kPa
C. 160 kPa
D. 240 kPa
E. 320 kPa

Problem 28Hard

The final state of a gas is $P_2=150\ \mathrm{kPa}$, $V_2=2.00\ \mathrm L$, and $T_2=400\ \mathrm K$. If the initial state has $V_1=3.00\ \mathrm L$ and $T_1=300\ \mathrm K$, what is $P_1$?

A. 50.0 kPa
B. 75.0 kPa
C. 100 kPa
D. 125 kPa
E. 200 kPa

Problem 29Hard

A gas in a closed rigid container is heated. Which statement is correct?

A. $P$ and $V$ decrease
B. $V$ and $n$ remain constant while $P$ increases
C. $P$ remains constant while $V$ increases
D. $n$ increases while $T$ remains constant
E. $V$ increases while $n$ decreases

Problem 30Hard

Approximately what volume does $0.400\ \mathrm{mol}$ of an ideal gas occupy at $27.0\,^{\circ}\mathrm C$ and $200\ \mathrm{kPa}$?

A. 2.50 L
B. 4.00 L
C. 5.00 L
D. 8.31 L
E. 10.0 L