A canister containing 115 kg of an ideal gas has a volume of 6.5 m³. If the gas exerts a pressure of 4.0 × 10⁵ Pa, what is the rms speed of the molecules?

Question

Quizplus · Accepted Answer

The rms speed of the molecules is given by:$$v_{rms}=\sqrt{\frac{3RT}{M}}$$where R is the gas constant, T is the temperature, and M is the molar mass of the gas.We can find the temperature of the gas using the ideal gas law:$$PV=nRT$$where P is the pressure, V is the volume, n is the number of moles of gas, and R is the gas constant.Solving for T, we get:$$T=\frac{PV}{nR}$$We can find the number of moles of gas using the molar mass:$$n=\frac{m}{M}$$where m is the mass of the gas and M is the molar mass.Substituting these expressions into the equation for the rms speed, we get:$$v_{rms}=\sqrt{\frac{3PVM}{mR}}$$Plugging in the given values, we get:$$v_{rms}=\sqrt{\frac{3(4.0	imes10^5	ext{ Pa})(6.5	ext{ m}^3)(115	ext{ kg})}{(115	ext{ kg})(8.31	ext{ J/mol K})}}$$$$v_{rms}=260	ext{ m/s}$$Therefore, the rms speed of the molecules is 260 m/s.

A Canister Containing 115 Kg of an Ideal Gas Has