Answer:
The metal has a molar mass of 65.37 g/mol
Explanation:
Step 1: Data given
Mass of the metal = 0.708 grams
Volume of hydrogen = 275 mL = 0.275 L
Atmospheric pressure = 1.0079 bar = 0.9947 atm
Temperature = 25°C
Vapor pressure of water at 25 °C = 0.03167 bar = 0.03126 atm
Step 2: The balanced equation
M(s) + H2SO4(aq) ⟶ MSO4 (aq) + H2(g)
Step 3: Calculate pH2
Atmospheric pressure = vapor pressure of water + pressure of H2
0.9947 atm = 0.03126 atm + pressure of H2
Pressure of H2 = 0.9947 - 0.03126
Pressure of H2 = 0.96344 atm
Step 4: Calculate moles of H2
p*V=n*R*T
⇒ with p = The pressure of H2 = 0.96344 atm
⇒ with V = the volume of H2 = 0.275 L
⇒ with n = the number of moles H2 = TO BE DETERMINED
⇒ with R = the gas constant = 0.08206 L*atm/K*mol
⇒ with T = the temperature = 25°C = 298 Kelvin
n = (p*V)/(R*T)
n = (0.96344 * 0.275)/(0.08206*298)
n = 0.01083 moles
Step 5: Calculate moles of M
For 1 mole of H2 produced, we need 1 mole M
For 0.0108 moles of H2 we need 0.01083 moles of M
Step 6: Calculate molar mass of M
Molar mass M = Mass M / moles M
Molar mass M = 0.708 grams / 0.01083 moles
Molar mass M = 65.37 g/mol
The metal has a molar mass of 65.37 g/mol
