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A 0.590 gram sample of a metal, M, reacts completely with sulfuric acid according to: M(s) +H2SO4(aq) --> MSO4(aq) +H2(g). A volume of 281 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.

Respuesta :

IthaloAbreu

Answer:

51.7 g/mol

Explanation:

Assuming hydrogen as an ideal gas, the ideal has equation is:

PV = nRT

Where P is the pressure, V is the volume, n is the number of moles, R is gas constant (R= 0.082 atm*L/mol*K), and T is the temperature.

P = 756 torr x [tex]\frac{1 atm}{760 torr}[/tex] = 0.995 atm

V = 281 mL = 0.281 L

T = 25ºC + 273 = 298 K

0.995x0.281 = nx0.082x298

24.436n = 0.2796

n = 0.0114 mol

For the reaction given, the stoichiometry is:

1 mol of M ------------ 1 mol of H₂

x               -------------- 0.0114 mol of H₂

By a simple direct three rule:

x = 0.0114 mol

The molar mass is the mass divided by the number of moles:

M = 0.590/0.0114

M = 51.7 g/mol

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