Question

Nitrogen was heated from 17°C to 37°C. The original volume of nitrogen was 8.5 L. Find the new volume in liters assuming P and n remain the same.

Answer 1

Answer:

The new volume of the gas is 9.086 liters.

Explanation:

Let suppose that nitrogen has a behavior of ideal gas, the equation of state for ideal gases is:

$P\cdot V = n \cdot R_{u}\cdot T$ (1)

Where:

$P$ - Pressure, measured in atmospheres.

$V$ - Volumen, measured in liters.

$n$ - Molar amount, measured in moles.

$T$ - Temperature, measured in Kelvin.

$R_{u}$ - Ideal gas constant, measured in atmosphere-liters per mole-Kelvin.

If pressure and molar amount of the gas remain constant, then we construct the following relationship:

$\frac{T_{1}}{V_{1}} = \frac{T_{2}}{V_{2}}$ (2)

If we know that $T_{1} = 290.15\,K$, $P_{1} = 8.5\,L$ and $T_{2} = 310.15\,K$, then the new volume of the gas is:

$V_{2} = \left(\frac{T_{2}}{T_{1}}\right)\cdot V_{1}$

$V_{2} = \left(\frac{310.15\,K}{290.15\,K} \right)\cdot (8.5\,L)$

$V_{2} = 9.086\,L$

The new volume of the gas is 9.086 liters.