Problem 71 - General Chemistry: Principles and Modern Applications

Question

At elevated temperatures, solid sodium chlorate \(\left(\mathrm{NaClO}_{3}\right)\) decomposes to produce sodium chloride, \(\mathrm{NaCl},\) and \(\mathrm{O}_{2}\) gas. A \(0.8765 \mathrm{g}\) sample of impure sodium chlorate was heated until the production of oxygen ceased. The oxygen gas was collected over water and occupied a volume of \(57.2 \mathrm{mL}\) at \(23.0^{\circ} \mathrm{C}\) and 734 Torr. Calculate the mass percentage of \(\mathrm{NaClO}_{3}\) in the original sample. Assume that none of the impurities produce oxygen on heating. The vapor pressure of water is 21.07 Torr at \(23^{\circ} \mathrm{C}\).

Step-by-Step Solution

Answer

The short answer will depend on the calculations made in the steps. The final value will be obtained after substituting the calculated values in the formula for mass percent. Make sure to express the final answer in percentage form.

Step 1: Calculation of Moles of \(\mathrm{O}_{2}\)

Firstly, calculate the number of moles of \(\mathrm{O}_{2}\) gas produced. Using the Ideal Gas Law, \(PV = nRT\), where P is the pressure, V is the volume, n is the number of moles, R is the gas law constant, and T is the temperature. Note that the pressure must be corrected for the presence of water vapor, therefore, the pressure of the collected oxygen is the total pressure minus the vapor pressure of the water. Convert the temperature from Celsius to Kelvin (K = C + 273). Substituting \(P = (734-21.07) Torr * (1 atm/760 Torr)\), \(V = 57.2 mL = 0.0572 L\), \(R = 0.08206 L.atm/K.mol\), and \(T = 23 + 273 = 296 K\) into the Ideal Gas Law and solve for n, number of moles.

Step 2: Calculation of Mass of \(\mathrm{NaClO}_{3}\)

The balanced chemical equation for the decomposition of sodium chlorate is \(\mathrm{2NaClO}_{3} \rightarrow \mathrm{2NaCl} + \mathrm{3O}_{2}\). This indicates that 2 moles of \(\mathrm{NaClO}_{3}\) produce 3 moles of \(\mathrm{O}_{2}\) gas. Therefore, the number of moles of \(\mathrm{NaClO}_{3}\) that decomposed can be calculated by multiplying the moles of \(\mathrm{O}_{2}\) produced (calculated in Step 1) by the ratio \((2/3)\). Once the moles of \(\mathrm{NaClO}_{3}\) is found, convert this to grams using the molar mass of \(\mathrm{NaClO}_{3}\) (106.44 g/mol).

Step 3: Calculation of Mass Percent of \(\mathrm{NaClO}_{3}\)

Finally, calculate the mass percentage of \(\mathrm{NaClO}_{3}\) in the original impure sample. The mass percentage is given by the formula: \((\text{Mass of} \ \mathrm{NaClO}_{3} / \text{Total Mass of Sample}) * 100\%\). The mass of \(\mathrm{NaClO}_{3}\) was calculated in Step 2 and the total mass of the sample is given as 0.8765 g. Substitute these values in the formula and solve to get the required mass percentage.

Key Concepts

Sodium Chlorate

Sodium chlorate, with the chemical formula \( \mathrm{NaClO}_{3} \), is a white crystalline compound that can decompose at elevated temperatures. During decomposition, sodium chlorate breaks down into sodium chloride (\( \mathrm{NaCl} \)) and releases oxygen gas (\( \mathrm{O}_{2} \)). This reaction is represented by the chemical equation:

• \( \mathrm{2NaClO}_{3} \rightarrow \mathrm{2NaCl} + \mathrm{3O}_{2} \)

Understanding this decomposition reaction is crucial for calculations in chemistry since it shows how sodium chlorate can be used to generate oxygen gas when heated. The proportion of products formed is significant as it helps in calculating the amount of reactant used and the resultant mass based on stoichiometry, which is essential for predicting the outcomes in chemical reactions. This knowledge plays a pivotal role in industries and laboratories where sodium chlorate serves as a source of oxygen and an oxidizing agent in various processes.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation that relates the pressure, volume, temperature, and number of moles of a gas. It is expressed as:

• \( PV = nRT \)

Here:

• \( P \) is the pressure of the gas.
• \( V \) is the volume it occupies.
• \( n \) is the number of moles of the gas.
• \( R \) is the ideal gas constant \( (0.08206 \, \text{L.atm/K.mol}) \).
• \( T \) is the temperature in Kelvin.

In the scenario of collecting oxygen gas from sodium chlorate decomposition, the Ideal Gas Law is utilized to determine the moles of \( \mathrm{O}_{2} \) produced. This calculation requires adjusting the measured pressure by subtracting the water vapor pressure, which accounts for the water overhead while collecting the gas. Additionally, converting the temperature to Kelvin ensures that the calculations adhere to the requirements of the Ideal Gas Law. Understanding and applying this law is critical in determining the behavior and quantity of gases under various conditions in both academic and practical applications.

Mass Percentage Calculation

Mass percentage is a way of expressing the concentration of a component in a mixture. To find the mass percentage of a substance in a sample, the formula is:

• \( \left(\frac{\text{Mass of the substance}}{\text{Total mass of the sample}}\right) \times 100\% \)

In the decomposition of sodium chlorate, this calculation is employed to determine how much of the original impure sample was pure sodium chlorate. After using stoichiometry to find how much sodium chlorate decomposed, the mass of \( \mathrm{NaClO}_{3} \) is compared to the total initial mass of the impure sample. This step illustrates the utility of mass percentage in gauging purity, a crucial factor in ensuring that chemical processes and reactions yield predictable and reliable results. Understanding mass percentage is vital for quality control and in confirming that the expected reactions occur with the anticipated efficiency in any given chemical task.