SAT Subject Test in Chemistry - Gas Laws

Suppose that an ideal gas at $0^{\circ}\text{C}$ and 2.0 atm has a volume of 11.2 cubic meters. Which of the following expressions represents the volume of the gas, in cubic meters, if the temperature were increased by $50^{\circ}\text{C}$ and the pressure decreased to 1.5 atm?

$11.2\text{ m}^3\times\frac{323\text{ K}}{273\text{ K}}\times\frac{2.0\text{ atm}}{1.5\text{ atm}}$

$11.2\text{ m}^3\times\frac{323\text{ K}}{273\text{ K}}\times\frac{1.5\text{ atm}}{2.0\text{ atm}}$

$11.2\text{ m}^3\times\frac{273\text{ K}}{323\text{ K}}\times\frac{2.0\text{ atm}}{1.5\text{ atm}}$

$11.2\text{ m}^3\times\frac{273\text{ K}}{323\text{ K}}\times\frac{1.5\text{ atm}}{2.0\text{ atm}}$

$11.2\text{ m}^3\times\frac{50\text{ K}}{0\text{ K}}\times\frac{1.5\text{ atm}}{2.0\text{ atm}}$

Explanation

First of all, the unit degrees Celsius should be converted to Kelvins by adding 273. This means that the temperature increases from 273 K to 323 K.

Next, the combined gas law can be used.

$\frac{P_1V_1}{T_1}=\frac{P_2V_2}{T_2}$

Plugging in the known values gives

$\frac{2.0\text{ atm}\times11.2\text{ m}^3}{273\text{ K}}=\frac{1.5\text{ atm}\times V_2}{323\text{ K}}$

and solving for the volume gives

$V_2=\frac{2.0\text{ atm}\times11.2\text{ m}^3\times323\text{ K}}{1.5\text{ atm}\times273\text{ K}}$

Rearranging shows this is clearly equivalent to the correct answer, $11.2\text{ m}^3\times\frac{323\text{ K}}{273\text{ K}}\times\frac{2.0\text{ atm}}{1.5\text{ atm}}$ .

Gas Laws

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