# A gas has a volume of 39 liters at STP. What will its volume be at 4 atm and 25°c?

May 30, 2017

$11 \text{L}$

#### Explanation:

We're asked to find the new volume of a gas after it is subdued to changes in pressure and temperature.

To solve this problem, we can use the combined gas law:

$\frac{{P}_{1} {V}_{1}}{{T}_{1}} = \frac{{P}_{2} {V}_{2}}{{T}_{2}}$

This equation allows us to find how one of these variables changes if the other two both change by known amounts.

The first thing we must do is convert the temperature from degrees Celsius to Kelvin:

$\text{K" = ""^"o""C" + 273 = 25^"o""C" + 273 = color(red)(298"K}$

Now, we have all our variables needed to solve this problem [remember that for standard temperature and pressure, $P = 1$ $\text{atm}$ and $T = 273$ "K"(0^"o""C")]. Let's rearrange this equation to solve for the final volume, ${V}_{2}$, and plug in our known variables:

V_2 = (P_1V_1T_2)/(P_2T_1) = ((1cancel("atm"))(39"L")(color(red)(298cancel("K"))))/((4cancel("atm"))(273cancel("K"))) = color(blue)(11"L")

The new volume of the gas after the changes in temperature and pressure will thus be $11 \text{L}$, rounded to two significant figures (the number given in the problem).