Question

Zinc ore (zinc sulphide) is treated with sulphuric acid, leaving a solution with some undissolved bits of material and releasing hydrogen sulphide gas. If \(10.8 \mathrm{~g}\) of zinc ore is treated with \(50.0 \mathrm{ml}\) of sulphuric acid (density \(1.2 \mathrm{~g} / \mathrm{ml}\) ), \(65.2 \mathrm{~g}\) of solution and undissolved material remains. In addition, hydrogen sulphide (density \(1.4 \mathrm{~g} / \mathrm{l}\) ) is evolved. What is the volume (in litres) of this gas? (a) \(4.0\) (b) \(5.6\) (c) \(7.84\) (d) \(4.4\)

Short answer

Answer: \(4 \mathrm{~l}\)

Step-by-step solution

Calculate the mass of the initial mixture

Add the mass of zinc ore and the mass of sulphuric acid to find the mass of the initial mixture. Mass of zinc ore = \(10.8 \mathrm{~g}\) Volume of sulphuric acid = \(50.0 \mathrm{~ml}\) Density of sulphuric acid = \(1.2 \mathrm{~g} / \mathrm{ml}\) First, we need to find the mass of sulphuric acid. Mass of sulphuric acid = Density of sulphuric acid * Volume of sulphuric acid Mass of sulphuric acid = \(1.2 \mathrm{~g} / \mathrm{ml} * 50.0 \mathrm{~ml} = 60 \mathrm{~g}\) Now, add the mass of zinc ore and sulphuric acid to find the mass of initial mixture. Mass of initial mixture = Mass of zinc ore + Mass of sulphuric acid Mass of initial mixture = \(10.8 \mathrm{~g} + 60 \mathrm{~g} = 70.8 \mathrm{~g}\)

Calculate the mass of dissolved zinc sulphide and hydrogen sulphide

Subtract the mass of the final mixture from the mass of the initial mixture to find the mass of dissolved zinc sulphide and hydrogen sulphide. Mass of final mixture = \(65.2 \mathrm{~g}\) Mass of dissolved zinc sulphide and hydrogen sulphide = Mass of initial mixture - Mass of final mixture Mass of dissolved zinc sulphide and hydrogen sulphide = \(70.8 \mathrm{~g} - 65.2 \mathrm{~g} = 5.6 \mathrm{~g}\)

Calculate the volume of hydrogen sulphide gas

Use the mass of hydrogen sulphide and its density to find the volume of the gas. Density of hydrogen sulphide = \(1.4 \mathrm{~g} / \mathrm{l}\) Mass of hydrogen sulphide = Mass of dissolved zinc sulphide and hydrogen sulphide (since only hydrogen sulphide gas is released) = \(5.6 \mathrm{~g}\) Volume of hydrogen sulphide = Mass of hydrogen sulphide / Density of hydrogen sulphide Volume of hydrogen sulphide = \(\frac{5.6 \mathrm{~g}}{1.4 \mathrm{~g} / \mathrm{l}} = 4 \mathrm{~l}\) The volume of hydrogen sulphide gas evolved is \(4 \mathrm{~l}\), which corresponds to option (a).

Key concepts

Chemical Reaction Calculations

Understanding chemical reaction calculations is crucial for solving problems like the one involving zinc ore and sulphuric acid. These calculations often begin with the mass of reactants. Here, we know the mass of zinc ore and can calculate the mass of sulphuric acid using its density and volume.

Mass and Density

To find the mass of sulphuric acid, we multiply the given density by the volume. The key concept here is that density is a compound's mass per unit volume. By combining mass measurements, we arrive at the total initial mass of reactants.

Reactants to Products

After reaction, we have a new mixture which includes undissolved materials and solutions. The difference in mass between the initial reactants and final mixture gives us the mass of evolved gas - in this case, hydrogen sulphide. Understanding that matter is conserved in a reaction, we can thus deduce the mass of products formed.

Mole Concept

The mole concept is a pillar of stoichiometry, representing a specific number (\(6.022 \times 10^{23}\) entities) of chemical units, be it atoms, molecules, ions, or electrons. Molar mass, the mass of one mole of a substance, plays a direct role in chemical reaction calculations.

When dealing with reactions, we often convert from grams to moles to use the coefficients of a balanced chemical equation to calculate reactant or product amounts. Even though this specific problem does not require converting to moles, understanding the mole concept helps in comprehending how chemists measure substances and predict the products of chemical reactions.

Chemical Equations

Chemical equations are symbolic representations of chemical reactions. They show the reactants transforming into products, with coefficients representing the number of moles that react or are produced. It is important for the equation to be balanced, meaning the number of atoms for each element is conserved before and after the reaction.

While the given problem does not include balancing the chemical equation, knowledge of balanced chemical equations could allow us to predict the relative amounts of reactants and products. For more complicated problems, understanding how to read and balance chemical equations is essential for predicting the amount of each reactant needed and the expected quantity of each product formed.