A 21-liter cylinder contains 1.5 moles of an ideal gas at 311 K. What is the pressure of the gas?

Question

Henry Antrim · Accepted Answer

#P = "1.8 atm"#

This practice problem for the ideal gas law equation is rather simple.

The ideal gas law equation appears like this, as you are aware.

#color(blue)(PV = nRT)" "#, where

#P# - the pressure of the gas #V# - the volume it occupies #n# - the number of moles of gas #R# - the universal gas constant, usually given as #0.0821 ("atm" * "L")/("mol" * "K")# #T# - the temperature of the gas, always expressed in Kelvin

Therefore, the issue gives you

Since you know the value of #R#, you can use this information to find the pressure #P#. First, rearrange the ideal gas law equation to isolate #P# on one side

#PV = nRT implies P = (nRT)/V#

Next, confirm that the units you were given correspond to those in the universal gas constant expression.

# {:(color(red)("Need"), color(white)(aaaaa), color(blue)("Have")), (color(white)(aaaa), color(white)(aaaa), color(white)(aaaa)), (color(white)(aa)"L", color(white)(aaaa), color(white)(aa)"L"color(white)(aaaaaa)color(green)(sqrt())), ("moles", color(white)(aaaa), "moles"color(white)(aaaaa)color(green)(sqrt())), (color(white)(aa)"K", color(white)(aaaa), color(white)(aa)"K"color(white)(aaaaaa)color(green)(sqrt())) :}#

The units given to you match those used for #R#, so you're good to go. Plug in your values to get

#P = (1.5 color(red)(cancel(color(black)("moles"))) * 0.0821("atm" * color(red)(cancel(color(black)("L"))))/(color(red)(cancel(color(black)("mol"))) * color(red)(cancel(color(black)("K")))) * 311color(red)(cancel(color(black)("K"))))/(21color(red)(cancel(color(black)("L"))))#

#P = "1.824 atm"#

The number of sig figs you have for the volume and number of moles of gas, rounded to two, is what the answer will be.

#P = color(green)("1.8 atm")#

Cooper Adams · Answer

undefined The pressure of the gas can be calculated using the ideal gas law equation:

$$PV = nRT$$

Where:
- $P$ is the pressure of the gas,
- $V$ is the volume of the gas (21 liters),
- $n$ is the number of moles of the gas (1.5 moles),
- $R$ is the ideal gas constant (0.0821 L·atm/(mol·K)),
- $T$ is the temperature of the gas in Kelvin (311 K).

Substitute the values into the equation and solve for $P$:

$$P = \frac{{nRT}}{V}$$

$$P = \frac{{(1.5\ \text{mol})(0.0821\ \text{L·atm/(mol·K)})(311\ \text{K})}}{21\ \text{L}}$$

$$P = \frac{{38.88455\ \text{L·atm}}}{21\ \text{L}}$$

$$P ≈ 1.85\ \text{atm}$$