Chapter 13.2, Problem 7RQ

Interpretation Introduction

Interpretation:

The balanced chemical equation for reaction between Mg and HCl needs to be determined. The volume of hydrogen gas needs to be determined after balancing the equation.

Concept Introduction:

Magnesium metal reacts with hydrochloric acid to produce hydrogen gas and magnesium chloride solution.

Answer to Problem 7RQ

The balanced chemical equation is-

  $\mathrm{Mg}(\mathrm{s})+2\mathrm{H}\mathrm{C}\mathrm{l}(\mathrm{g})\to \mathrm{M}\mathrm{g}\mathrm{C}{\mathrm{l}}_2(\mathrm{a}\mathrm{q})+{\mathrm{H}}_2(\mathrm{g})\uparrow$

The volume of hydrogen gas is 10.05 litre.

Explanation of Solution

Given information: Mass of magnesium is 10 g

Pressure of hydrogen gas is 1.00 atm

Temperature is 25 °C or, 298 K

Calculation:

The balanced chemical equation is-

  $\mathrm{Mg}(\mathrm{s})+2\mathrm{H}\mathrm{C}\mathrm{l}(\mathrm{g})=\mathrm{M}\mathrm{g}\mathrm{C}{\mathrm{l}}_2(\mathrm{a}\mathrm{q})+{\mathrm{H}}_2(\mathrm{g})\uparrow$

Number of moles of magnesium can be calculated as follows:

  $\begin{array}{c}\mathrm{n}=\frac{10\text{ g}}{24.3\text{ g/mol}}\\ =0.412\text{ mol}\end{array}$

From balanced reaction, 1 mol of Mg gives 1 mol of hydrogen gas.

So, number of moles of hydrogen will be 0.412 mol.

The ideal gas equation is represented as follows:

  $\mathrm{P}\mathrm{V}=\mathrm{n}\mathrm{R}\mathrm{T}$

Or,

  $\begin{array}{c}\mathrm{V}=\frac{\mathrm{n}\mathrm{R}\mathrm{T}}{\mathrm{P}}\\ =\frac{0.412\mathrm{m}\mathrm{o}\mathrm{l}\times 0.082\mathrm{L}\mathrm{a}\mathrm{t}\mathrm{m}/\mathrm{m}\mathrm{o}\mathrm{l}\mathrm{K}\times 298\mathrm{K}}{1.00\mathrm{a}\mathrm{t}\mathrm{m}}\\ =10.05\mathrm{L}\end{array}$