A small bottle of nitrogen gas, volume 6.5 dm³ is stored at 22 °C and a pressure of 63 bar. Calculate the pressure (in bar) inside the bottle when the temperature increases to 28 °C; assume the gas behaves as an ideal gas.

Question

Quizplus · Accepted Answer

We can use the ideal gas law to solve for the new pressure:

PV = nRT

where P is the pressure, V is the volume, n is the number of moles of gas, R is the gas constant, and T is the temperature in Kelvin.

We can first find the number of moles of gas using the given volume and pressure:

n = PV/RT

where we can convert the given temperature to Kelvin (22 °C + 273.15 = 295.15 K) and use the gas constant R = 0.08314 L bar mol^-1 K^-1.

n = (63 bar * 6.5 dm^3) / (0.08314 L bar mol^-1 K^-1 * 295.15 K)

n = 1.79 mol

We can then use the ideal gas law again to solve for the new pressure, with the volume and number of moles remaining constant but the temperature increasing to 28 °C (28 °C + 273.15 = 301.15 K):

P new = nRT new / V

P new = (1.79 mol * 0.08314 L bar mol^-1 K^-1 * 301.15 K) / 6.5 dm^3

P new = 64.28 bar

Therefore, the answer is D) 64.28.

A Small Bottle of Nitrogen Gas, Volume 6