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Chapter 5: Problem 167

Zinc and magnesium metal each reacts with hydrochloric acid to make chloride salts of the respective metals, and hydrogen gas. A 10.00-g mixture of zinc and magnesium produces \(0.5171 \mathrm{g}\) of hydrogen gas upon being mixed with an excess of hydrochloric acid. Determine the percent magnesium by mass in the original mixture.

Short Answer

Expert verified
The percentage of magnesium by mass in the original mixture is \(24.46\%\).

Step by step solution

01

Write balanced chemical equations for the reactions of zinc and magnesium with hydrochloric acid.

Write the balanced chemical equations for the reactions of zinc and magnesium with hydrochloric acid. The equations are: \(Zn + 2HCl \rightarrow ZnCl_2 + H_2\) \(Mg + 2HCl \rightarrow MgCl_2 + H_2\)
02

Calculate the moles of hydrogen gas produced.

Using the molar mass of hydrogen gas, we can calculate the moles of hydrogen gas produced. Molar mass of \(H_2 = 2.016 \mathrm{g/mol}\) Moles of hydrogen gas \((n_{H}) = \frac{0.5171 \mathrm{g}}{2.016 \mathrm{g/mol}} = 0.2567 \mathrm{mol}\)
03

Calculate the moles of zinc and magnesium using stoichiometry.

Using the stoichiometry of the balanced chemical equations, we can calculate the moles of zinc and magnesium that reacted. Let's assume that x moles of zinc reacted and y moles of magnesium reacted. Since both zinc and magnesium produce 1 mole of hydrogen gas for each mole reacted, we can write: \(x + y = n_{H} = 0.2567\)
04

Calculate the mass of zinc and magnesium using their molar masses.

Using the molar masses of zinc and magnesium, we can write the equations: Mass of zinc \(= x \times M_{Zn}\) , where \(M_{Zn} = 65.38 \mathrm{g/mol}\) Mass of magnesium \(= y \times M_{Mg}\) , where \(M_{Mg} = 24.305 \mathrm{g/mol}\) The total mass of the mixture is 10.00 g, which means: \(x \times M_{Zn} + y \times M_{Mg} = 10.00\)
05

Solve the equations to find the moles of zinc and magnesium.

We have two equations with two variables. We can solve them using the substitution or elimination method. - \(x + y = 0.2567\) - \(x \times 65.38 + y \times 24.305 = 10.00\) Let's solve for x in the first equation, and substitute it in the second equation: \[x = 0.2567 - y\] \((0.2567 - y) \times 65.38 + y \times 24.305 = 10.00\) Now, solving this equation for y, we find that: \(y = 0.1007\, \mathrm{mol}\) Using y and the first equation, we can find x: \(x = 0.2567 - 0.1007 = 0.156\, \mathrm{mol}\)
06

Calculate the mass of magnesium in the original mixture and the percentage by mass.

Now that we have the moles of magnesium (y), we can find the mass of magnesium in the original mixture: Mass of magnesium \(= y \times M_{Mg} = 0.1007 \times 24.305 = 2.446 \mathrm{g}\) Finally, we can calculate the percentage by mass of magnesium in the original mixture: Percentage of magnesium \(= \frac{2.446}{10.00} \times 100 = 24.46 \%\)

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Most popular questions from this chapter

Give the balanced equation for each of the following chemical reactions: a. Glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\) reacts with oxygen gas to produce gaseous carbon dioxide and water vapor. b. Solid iron(III) sulfide reacts with gaseous hydrogen chloride to form solid iron(III) chloride and hydrogen sulfide gas. c. Carbon disulfide liquid reacts with ammonia gas to produce hydrogen sulfide gas and solid ammonium thiocyanate \(\left(\mathrm{NH}_{4} \mathrm{SCN}\right).\)

Terephthalic acid is an important chemical used in the manufacture of polyesters and plasticizers. It contains only \(\mathrm{C}, \mathrm{H}\) and O. Combustion of \(19.81 \mathrm{mg}\) terephthalic acid produces \(41.98 \mathrm{mg} \mathrm{CO}_{2}\) and \(6.45 \mathrm{mg} \mathrm{H}_{2} \mathrm{O} .\) If 0.250 mole of terephthalic acid has a mass of \(41.5 \mathrm{g},\) determine the molecular formula for terephthalic acid.

One of relatively few reactions that takes place directly between two solids at room temperature is $$\begin{aligned}\mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}(s)+\mathrm{NH}_{4} \mathrm{SCN}(s) & \longrightarrow \\\\\mathrm{Ba}(\mathrm{SCN})_{2}(s) &+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{NH}_{3}(g)\end{aligned}$$ In this equation, the \(\cdot 8 \mathrm{H}_{2} \mathrm{O}\) in \(\mathrm{Ba}(\mathrm{OH})_{2} \cdot 8 \mathrm{H}_{2} \mathrm{O}\) indicates the presence of eight water molecules. This compound is called barium hydroxide octahydrate. a. Balance the equation. b. What mass of ammonium thiocyanate \(\left(\mathrm{NH}_{4} \mathrm{SCN}\right)\) must be used if it is to react completely with 6.5 g barium hydroxide octahydrate?

Determine the molecular formula of a compound that contains \(26.7 \% \mathrm{P}, 12.1 \% \mathrm{N},\) and \(61.2 \% \mathrm{Cl},\) and has a molar mass of \(580 \mathrm{g} / \mathrm{mol}.\)

A compound contains \(47.08 \%\) carbon, \(6.59 \%\) hydrogen, and \(46.33 \%\) chlorine by mass; the molar mass of the compound is 153 g/mol. What are the empirical and molecular formulas of the compound?
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