Question

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

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

Step-by-step solution

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: \(Zn + 2HCl \rightarrow ZnCl_2 + H_2\) \(Mg + 2HCl \rightarrow MgCl_2 + H_2\)

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 \((n_{H}) = \frac{0.5171 \mathrm{g}}{2.016 \mathrm{g/mol}} = 0.2567 \mathrm{mol}\)

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: \(x + y = n_{H} = 0.2567\)

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: \(x \times M_{Zn} + y \times M_{Mg} = 10.00\)

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: \(x = 0.2567 - 0.1007 = 0.156\, \mathrm{mol}\)

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 \(= \frac{2.446}{10.00} \times 100 = 24.46 \%\)

Key concepts

Chemical Reactions

In the realm of chemistry, reactions occur when substances undergo a chemical change to form new products. This change involves making and breaking chemical bonds, which is a fundamental concept in stoichiometry. When dealing with chemical reactions like those of zinc and magnesium with hydrochloric acid, the substances involved undergo a transformation.

• Zinc reacts with hydrochloric acid to form zinc chloride and hydrogen gas.
• Magnesium reacts similarly to produce magnesium chloride and hydrogen gas.

Understanding these reactions helps to predict the products formed and the quantities involved. It also involves looking at reactants and products and balancing equations to ensure that matter is conserved. This is crucial for calculating how much product can be formed from given amounts of reactants.

Molar Mass

Molar mass is an essential concept in understanding how much of a substance is involved in a reaction. It is defined as the mass of one mole of a substance, usually expressed in grams per mole (g/mol). It serves as a bridge between the mass of substances and the quantity of molecules or atoms they contain.
For example, the molar mass of hydrogen gas (\( H_2 \)) is 2.016 g/mol, which tells us how much one mole of hydrogen gas weighs. Similarly, zinc (Zn) has a molar mass of 65.38 g/mol, and magnesium (Mg) has a molar mass of 24.305 g/mol.

• Molar mass allows the conversion of grams to moles and vice versa.
• It connects the mass of reactants subject to reactions with the expected yield of products.

Knowing these values is crucial for calculating the amounts of each substance used and produced in a reaction, which is often pivotal in determining the stoichiometry of the equation.

Percent Composition

Percent composition refers to the percent by mass of each element present in a compound or a mixture. It is an important concept in chemistry as it provides information about the relative amounts of different elements within a substance.

• To find the percent composition, divide the mass of the desired component by the total mass of the mixture or compound, then multiply by 100.
• It provides insight into the makeup of materials, such as the percentage of magnesium in a mixture of metals.

This concept is handy in experimental chemistry where compositions of unknown substances need to be determined. For our problem, calculating the percent composition of magnesium in the mixture involves determining the mass of magnesium and dividing it by the total mass of the mixture before multiplying it by 100 to obtain the percentage.

Balanced Equations

Balanced equations are essential for accurately describing chemical reactions. A balanced chemical equation has an equal number of atoms for each element involved on both sides of the equation, reflecting the law of conservation of mass.

• When writing balanced equations, subscripts and coefficients are used to show the number of atoms and molecules.
• It's critical to ensure that the same amount and type of atoms are present before and after a reaction.

For example, the balanced equation for the reaction of zinc with hydrochloric acid is:\[Zn + 2HCl \rightarrow ZnCl_2 + H_2\]This means one atom of zinc reacts with two molecules of hydrochloric acid to produce one molecule of zinc chloride and one molecule of hydrogen. Similar balancing is applied to the magnesium reaction:\[Mg + 2HCl \rightarrow MgCl_2 + H_2\]
By understanding balanced equations, we can calculate the exact amounts of reactants needed and products formed, which is vital for stoichiometric calculations.