Ten moles of a gas are contained in a 1.00 L container at 295 K. What is the pressure of the gas?

Aug 17, 2017

$P = 242$ $\text{atm}$

Explanation:

We're asked to find the pressure of a gas, given its temperature, and volume, and number of moles.

We can use the ideal-gas equation:

ul(PV = nRT

where

• $P$ is the pressure of the gas (what we're trying to find)

• $V$ is the volume occupied by the gas (given as $1.00$ $\text{L}$

• $n$ is the number of moles of gas present (given as $10$ $\text{mol}$)

• $R$ is the universal gas constant, equal to $0.082057 \left(\text{L"·"atm")/("mol"·"K}\right)$

• $T$ is the absolute temperature of the gas (which must be in units of kelvin), given as $295$ $\text{K}$

Let's rearrange the above equation to solve for the pressure, $P$:

$P = \frac{n R T}{V}$

Plugging in known values:

color(red)(P) = ((10cancel("mol"))(0.082057(cancel("L")·"atm")/(cancel("mol")·cancel("K")))(295cancel("K")))/(1.00cancel("L")) = color(red)(ulbar(|stackrel(" ")(" "242color(white)(l)"atm"" ")|)

The pressure is thus color(red)(242color(white)(l)"atmospheres".