Question

Chlorine dioxide, \(\mathrm{ClO}_{2}\), is sometimes used as a chlorinating agent for water treatment. It can be prepared from the reaction below: \(\mathrm{Cl}_{2}(\mathrm{g})+4 \mathrm{NaClO}(\mathrm{aq}) \longrightarrow 4 \mathrm{NaCl}(\mathrm{aq})+2 \mathrm{ClO}_{2}(\mathrm{g})\) In an experiment, \(1.0 \mathrm{L} \mathrm{Cl}_{2}(\mathrm{g}),\) measured at \(10.0^{\circ} \mathrm{C}\) and 4.66 atm, is dissolved in 0.750 L of 2.00 M \(\mathrm{NaClO}(\mathrm{aq}) .\) If \(25.9 \mathrm{g}\) of pure \(\mathrm{ClO}_{2}\) is obtained, then what is the percent vield for this experiment?

Short answer

The percent yield of \(ClO_2(g)\) in this experiment can be calculated using the procedure outlined in steps 1-4.

Step-by-step solution

Calculate number of moles of \(Cl_2(g)\)

Start by calculating the number of moles of \(Cl_2(g)\). The Ideal Gas Law (PV = nRT) can be used here, where P is the pressure (4.66 atm), V is the volume (1.0 L), R is the gas constant (0.0821 atm·L/mol·K) and T is the temperature (283.15 K as we need to convert the degrees celsius to Kelvin by adding 273.15). So the equation becomes: n = PV/RT

Calculate moles of \(ClO_2(g)\) expected (theoretical yield)

The stoichiometry of the reaction shows that two moles of \(ClO_2(g)\) are produced per one mole of \(Cl_2(g)\). Hence, the number of moles of \(ClO_2(g)\) that theoretically can be produced is double that of \(Cl_2(g)\). Multiply the moles of \(Cl_2(g)\) obtained from step 1 by 2 to get the theoretical yield in moles of \(ClO_2(g)\).

Calculate the actual yield of \(ClO_2(g)\)

For determining the actual yield, convert the mass of \(ClO_2(g)\) obtained (25.9 g) into moles using its molar mass (67.45 g/mol). The formula for this is: moles = mass/molar mass.

Calculate percent yield

To calculate the percent yield, divide the actual yield of \(ClO_2(g)\) (from step 3) by the theoretical yield of \(ClO_2(g)\) (from step 2) and then multiply by 100.

Key concepts

Chlorine Dioxide Preparation

Chlorine dioxide (\(\text{ClO}_2\)) is an important chemical compound frequently used for disinfecting drinking water and treating wastewater. It is effective in killing bacteria, viruses, and other microorganisms. To prepare chlorine dioxide, react chlorine gas (\(\text{Cl}_2\)) with sodium chlorite (\(\text{NaClO}\)) in aqueous solution. The chemical equation for this reaction is: \(\text{Cl}_2(g) + 4 \text{NaClO}(aq) \rightarrow 4 \text{NaCl}(aq) + 2 \text{ClO}_2(g)\).

In this experiment, chlorine acts as a reactant, while sodium chlorite serves as a catalyst. When balancing chemical reactions, it's crucial to verify that the number of atoms for each element is the same on both sides. This ensures the reaction complies with the law of conservation of mass.

Keep in mind that chemical synthesis is influenced by temperature, pressure, and concentration. For \(\text{ClO}_2\), optimal conditions enhance yield and efficiency. The reaction must be controlled to avoid runaway reactions, due to the volatile nature of chlorine dioxide.

Ideal Gas Law

The Ideal Gas Law is a fundamental principle in chemistry describing the behavior of gases. It is expressed by the equation: \(PV = nRT\). Here, \(P\) stands for pressure, \(V\) is volume, \(n\) represents the number of moles, \(R\) is the ideal gas constant (\(0.0821 \text{ atm} \cdot \text{L}/\text{mol} \cdot \text{K}\)), and \(T\) the temperature in Kelvin.

For converting Celsius to Kelvin, add 273.15 to the Celsius temperature. In our example, at \(10.0^{\circ} \text{C}\), the Kelvin temperature is \(283.15 \text{ K}\). By substituting the values, you can calculate the number of moles of \(\text{Cl}_2(g)\) using the formula \(n = \frac{PV}{RT}\). This equation allows you to relate the physical properties of gases with their reactions.

The Ideal Gas Law is an approximation that works best at high temperature and low pressure, but it serves as a useful tool for predicting the behavior of gases under normal conditions. It helps chemists to understand and predict results in chemical reactions involving gases.

Stoichiometry in Chemistry

Stoichiometry is the study of quantitative relationships in chemical reactions. It helps chemists calculate the amounts of reactants and products involved in a chemical reaction.

In the preparation of chlorine dioxide, stoichiometry is used to determine the theoretical yield of \(\text{ClO}_2\) from a known quantity of \(\text{Cl}_2\). For every mole of \(\text{Cl}_2\) reacted, two moles of \(\text{ClO}_2\) are produced. This stoichiometric ratio shows that the number of moles of \(\text{ClO}_2\) is double that of \(\text{Cl}_2\).

To find the percent yield, compare the actual yield obtained from the experiment to the theoretical yield calculated through stoichiometry. Use the formula: \(\text{Percent Yield} = \left(\frac{\text{Actual Yield}}{\text{Theoretical Yield}}\right) \times 100\) to determine efficiency.

Stoichiometry is crucial for optimizing reactions, minimizing waste, and calculating precise amounts needed for industrial applications. Being proficient in stoichiometry allows scientists to plan and conduct experiments with accuracy and predict the outcomes.