5.8 ~g of a gas maintained at 95^ C occupies the same volume as 0.368 ~g of hydrogen gas maintained at a temperature of 17^ C and pressure being the same atmospheric pressure for both the gases. What is the molecular mass of the unknown gas?

Step-by-step solution

Using the ideal gas equation PV = nRT , where n = w M , we have V = wRT PM . Since the volume V and pressure P are the same for both gases, we can write the equality: w₁ R T₁ M₁ P = w₂ R T₂ M₂ P Canceling R and P from both sides, we get: w₁ T₁ M₁ = w₂ T₂ M₂ Given values for the unknown gas: w₁ = 5.8 g , T₁ = 95 + 273 = 368 K . Given values for hydrogen gas ( H₂ ): w₂ = 0.368 g , T₂ = 17 + 273 = 290 K , M₂ = 2 g/mol . Substituting these values into the equation: 5.8 368 M₁ = 0.368 290 2 Solving for M₁ : M₁ = 5.8 368