A gas sample of #Xe# occupies 10-liter balloon at 27°C under a pressure of 1.2 atm. Approximately what volume would the gas occupy at 350 K at 2 atm of pressure?

Question

Mateo Aguilar · Accepted Answer

The gas would occupy approximately 7 L.

An illustration of a Combined Gas Laws problem is this one. #color(blue)(|bar(ul((P_1V_1)/T_1 = (P_2V_2)/T_2|)# This formula can be rearranged to get #V_2 = V_1 × P_1/P_2 × T_2/T_1# Your information is: #P_1 = "1.2 atm"; V_1 = "10 L"; T_1 = "(27 + 273.15) K" ="300.15 K"# #P_2 = "2 atm";color(white)(m) V_2 = "?";color(white)(ml) T_2 = "350 K"# #V_2 = V_1 × P_1/P_2 × T_2/T_1 = "10 L" × (1.2 color(red)(cancel(color(black)("atm"))))/(2 color(red)(cancel(color(black)("atm")))) × (350 color(red)(cancel(color(black)("K"))))/(300.15 color(red)(cancel(color(black)("K")))) = "7 L"# It has a volume of about 7 L.

Serenity Allen · Answer

undefined To solve this problem, we can use the combined gas law, which states that the ratio of the initial pressure to the initial temperature is equal to the ratio of the final pressure to the final temperature, assuming the amount of gas and the volume remain constant.

$ \frac{P_1 \times V_1}{T_1} = \frac{P_2 \times V_2}{T_2} $

Given:
$P_1 = 1.2 \text{ atm}$ (initial pressure)
$V_1 = 10 \text{ L}$ (initial volume)
$T_1 = 27°C = 300 \text{ K}$ (initial temperature)
$P_2 = 2 \text{ atm}$ (final pressure)
$T_2 = 350 \text{ K}$ (final temperature)

We need to find $V_2$, the final volume.

Rearranging the equation, we get:

$V_2 = \frac{P_1 \times V_1 \times T_2}{P_2 \times T_1}$

Substituting the given values:

$V_2 = \frac{(1.2 \text{ atm}) \times (10 \text{ L}) \times (350 \text{ K})}{(2 \text{ atm}) \times (300 \text{ K})}$

$V_2 = \frac{(12 \times 350)}{(2 \times 3)}$

$V_2 = \frac{4200}{6}$

$V_2 = 700 \text{ L}$

Therefore, the gas would occupy approximately 700 liters at 350 K and 2 atm of pressure.