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

Answer:

The pressure inside the cylinder is $8.327\times 10^{-3}$ atmospheres.

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

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 $R_{u} = 0.082\,\frac{atm\cdot L}{mol\cdot K}$, then the pressured inside the cylinder is:

$P = \frac{n\cdot R_{u}\cdot T}{V}$

$P = \frac{(0.020\,mol)\cdot \left(0.082\,\frac{atm\cdot L}{mol\cdot K}\right)\cdot (304.65\,K) }{60\,L}$

$P = 8.327\times 10^{-3}\,atm$

The pressure inside the cylinder is $8.327\times 10^{-3}$ atmospheres.

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