Question

When a cylinder of helium gas is left standing in the sun, the temperature of the helium reaches 31.5C. The cylinder has a volume of 60.0 L and contains 0.020 mol of helium. What is the pressure in atmospheres inside the cylinder? What is the value for R for this problem?

Answer 1

The pressure inside the cylinder is
`8.327* 10^(-3)` atmospheres.

The value for R for this problem is 0.082 atmosphere-liters per mol-Kelvin.

Step-by-step explanation:

Let suppose that helium gas inside the cylinder behaves as an ideal gas, the equation of state for the ideal gas is:

`P\cdot V = n\cdot R_(u)\cdot T` (1)

Where:

`P` - Pressure, measured in atmospheres.

`V` - Volume, measured in liters.

`n` - Molar quantity, measured in moles.

`T` - Temperature, measured in Kelvin.

`R_(u)` - Ideal gas, measured in atmosphere-liters per mole-Kelvin.

If we know that
`V = 60\,L`,
`n = 0.020\,mol`,
`T = 304.65\,K` and
`R_(u) = 0.082\,(atm\cdot L)/(mol\cdot K)`, then the pressured inside the cylinder is:

`P = (n\cdot R_(u)\cdot T)/(V)`

`P = ((0.020\,mol)\cdot \left(0.082\,(atm\cdot L)/(mol\cdot K)\right)\cdot (304.65\,K) )/(60\,L)`

`P = 8.327* 10^(-3)\,atm`

The pressure inside the cylinder is
`8.327* 10^(-3)` atmospheres.

The value for R for this problem is 0.082 atmosphere-liters per mol-Kelvin.