A closed vessel contains a mixture of 1 g of He and 4 g of CH ₄ gases at a pressure of 100 kPa . If the root-mean-square speed of the He atoms in the mixture is 1500 m/s , the volume of the vessel is:

Step-by-step solution

The root-mean-square speed of a gas is given by v_ rms = 3RT M For Helium, the molar mass M = 4 g/mol = 0.004 kg/mol . Given v_ rms = 1500 m/s , we can find the value of RT : 1500 = 3RT 0.004 Squaring both sides: 2250000 = 3RT 0.004 3RT = 2250000 0.004 = 9000 RT = 3000 J/mol Now, calculate the total number of moles in the gas mixture: Moles of He = 1 4 = 0.25 Moles of CH ₄ = 4 16 = 0.25 Total moles n = 0.25 + 0.25 = 0.5 moles Using the ideal gas equation PV = nRT to find the volume V : V = nRT P Substituting the kn