Magnesium metal reacts with hydrochloric acid to form aqueous magnesium chloride and hydrogen gas. An excess of magnesium is reacted with 20.0 mL of 3.00 M hydrochloric acid, and all of the hydrogen is collected in a balloon at 25°C and 1.00 atm. What is the expected volume of the balloon?

Question

Quizplus · Accepted Answer

First, we need to find the moles of hydrogen gas produced in the reaction. From the balanced chemical equation:
Mg (s) + 2 HCl (aq) → MgCl2 (aq) + H2 (g)

We can see that 1 mole of magnesium reacts with 2 moles of hydrochloric acid to produce 1 mole of hydrogen gas. Since we have an excess of magnesium, we only need to consider the hydrochloric acid. Using the given volume and concentration of hydrochloric acid, we can calculate the moles of hydrochloric acid present:

moles HCl = volume x concentration = 20.0 mL x 0.00300 mol/mL = 0.0600 mol HCl

Since there is a 1:2 ratio between HCl and H2, the moles of hydrogen gas produced is:

moles H2 = 0.5 x 0.0600 mol = 0.0300 mol H2

Next, we can use the ideal gas law to calculate the volume occupied by the hydrogen gas at the given temperature and pressure:

PV = nRT

V = nRT/P

where P = 1.00 atm, T = 25°C + 273 = 298 K, R = 0.0821 L·atm/K·mol, and n = 0.0300 mol

V = (0.0300 mol) (0.0821 L·atm/K·mol) (298 K) / (1.00 atm)

V = 0.734 L

Therefore, the expected volume of the balloon is 0.734 L, which is choice A.

Magnesium Metal Reacts with Hydrochloric Acid to Form Aqueous Magnesium