Question

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

Answer 1

`P = 242` `"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` `"L"`

• `n` is the number of moles of gas present (given as `10` `"mol"`)

• `R` is the universal gas constant, equal to `0.082057("L"·"atm")/("mol"·"K")`

• `T` is the absolute temperature of the gas (which must be in units of kelvin), given as `295` `"K"`

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

`P = (nRT)/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"`.