Question

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< Question 18 of 19 > A 0.678 g sample of a metal, M, reacts completely with sulfuric acid according to M(s) +H,SO, (aq) — MSO, (aq) +Hy(Ⓡ) A volume of 293 mL of hydrogen is collected over water, the water level in the collecting vessel is the same as the outside level. Atmospheric pressure is 756.0 Torr, and the temperature is 25 "C. Calculate the molar mass of the metal. molar mass: 67.8

Answer 1

The Dalton's law state that the total pressures of a solution are equal to the sum of partial pressure of each component of the solution. Protal = PA + P3+ PC ...... (1) Where, the total pressure of the mixture is denoted by Protal, the partial pressure of component A, B, and C are denoted by PA, Pg, and Pc respectively. The given total pressure is 756 torr. Therefore, it is the sum of pressure of water vapor which is constant as 23.8 torr, and the pressure of gas represented as follows: Protal = PGas + PVapor pressure of water Substituting, the above values to calculate the pressure of hydrogen gas as follows: 756 torr = PGas +23.8torr PGas =(756–23.8) torr = 732.2 toir Now, from the ideal gas equation which is as follows: PV=nRT The given values are as follows: Number of moles(n)= ..?? Gas constant (R)= 62.4L.toir.K mol Temperature (T)= (25+273) = 298K Volume 293mL (V)=0.293L Pressure (P)= 732.2 torr To find the molar mass of unknown gas, substitute the given values in equation (1), as follows: 732.2 tort 0.293 L =n X62.4L.torr.K mol-1 x 298 K 732.2x0.293 n = 62.4x 298 = 0.011537mol Hence, the molar moles of unknown metal are 0.011537mol. Hence the one mole of a compound contains its molecular weight in gram per mole. Therefore, convert the gram of hydrogen into mole as follows: Given Mass of M Molecular masss of M =- Moles of M 0.678g. molt 0.011537 pol = 58.77 g Hence, the molecular mass of unknown metal i