Mg + 2 H+(aq) Mg2+ (aq) + H2 (g) If 0.883 g of magnesium is added to 25.5 mL of 1.345 M HCl solution at 25°C and 1.00 atm, how many liters will be occupied by the dry hydrogen gas which is produced?

Question

The vapor pressure of water at 25°C is 3.2 kPa.

Answer 1

Mg(s) + 2H⁺(aq) ==> Mg²⁺(aq) + H₂(g) ... balanced equation

Before we can determine the volume of the H₂ gas, we first must find how many moles of H₂ gas are formed. To do this, we first have to determine which, if any, reactant is present in limiting supply. A simple way to find the limiting reactant is to divide the moles of each reactant by its corresponding coefficient in the balanced equation.

For Mg, we have: 0.883 g x 1 mol Mg / 24.3 g = 0.0363 mols (÷1->0.0363)

For H⁺, we have: 25.5 mls x 1 L/1000 mls x 1.345 mol/L = 0.0343 mols H⁺ (÷2->0.017)

Thus, H⁺ is limiting (0.017 is less than 0.036) and H⁺ will determine how many moles H₂ gas will form.

Using dimensional analysis and the mole ratios in the balanced equation, we find mols H₂ formed:

0.0343 mol H⁺ x 1 mol H₂ / 2 mol H⁺ = 0.0171 moles H₂ formed

Now we can use the ideal gas law (PV = nRT) to find the volume in liters of 0.0171 moles H₂ gas. But first, we must do a few simple conversions/calculations.

The pressure is give as 1 atm and the temperature is 25ºC. The vapor pressure of water at 25ºC is given as 3.2kPa. We must convert 3.2 kPa to atmospheres and 25ºC to Kelvin. We must also subtract the vapor pressure of water at 25º from the 1 atm pressure in the atmosphere.

Converting 3.2 kPa to atm: 3.2 kPa x 1 atm / 101.325 kPa = 0.0316 atm

Converting 25ºC to Kelvin: 25 + 273 = 298K

Subtracting vapor pressure of water from 1 atm: 1 atm - 0.0316 atm = 0.9684 atm = P

Now we can use the ideal gas law to solve for V (volume in liters):

PV = nRT

P = pressure =0.9684 atm

V = ?

n = moles = 0.0171 (see above for the calculation of moles)

R = gas constant = 0.0821 Latm/Kmol

T = temperature = 298K

Solving for V, we have...

V = nRT/P = (0.0171)(0.0821)(298) / (0.9684)

V = 0.432 Liters