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Chapter 6: Problem 71

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 \(23^{\circ} \mathrm{C}\).

Short Answer

Expert verified
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 by step solution

01

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.
02

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).
03

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.

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Most popular questions from this chapter

A gaseous hydrocarbon that is \(82.7 \%\) C and \(17.3 \%\) H by mass has a density of \(2.35 \mathrm{g} / \mathrm{L}\) at \(25^{\circ} \mathrm{C}\) and 752 Torr. What is the molecular formula of this hydrocarbon?

A mixture of \(1.00 \mathrm{g} \mathrm{H}_{2}\) and \(8.60 \mathrm{g} \mathrm{O}_{2}\) is introduced into a 1.500 L flask at \(25^{\circ} \mathrm{C}\). When the mixture is ignited, an explosive reaction occurs in which water is the only product. What is the total gas pressure when the flask is returned to \(25^{\circ} \mathrm{C} ?\) (The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is \(23.8 \mathrm{mmHg}\).)

A particular coal sample contains \(3.28 \%\) S by mass. When the coal is burned, the sulfur is converted to \(\mathrm{SO}_{2}(\mathrm{g}) .\) What volume of \(\mathrm{SO}_{2}(\mathrm{g}),\) measured at \(23^{\circ} \mathrm{C}\) and \(738 \mathrm{mm} \mathrm{Hg},\) is produced by burning \(1.2 \times 10^{6} \mathrm{kg}\) of this coal?

When solid \(\mathrm{KClO}_{3}\) is heated strongly, it decomposes to form solid potassium chloride, \(\mathrm{KCl}\), and \(\mathrm{O}_{2}\) gas. \(\mathrm{A}\) \(0.415 \mathrm{g}\) sample of impure \(\mathrm{KClO}_{3}\) is heated strongly and the \(\mathrm{O}_{2}\) gas produced by the decomposition is collected over water. When the wet \(\mathrm{O}_{2}\) gas is cooled back to \(26^{\circ} \mathrm{C}\), the total volume is \(229 \mathrm{mL}\) and the total pressure is 323 Torr. What is the mass percentage of \(\mathrm{KClO}_{3}\) in the original sample? Assume that none of the impurities produce oxygen on heating. The vapor pressure of water is 25.22 Torr at \(26^{\circ} \mathrm{C}\).

A 0.7178 g sample of a hydrocarbon occupies a volume of \(390.7 \mathrm{mL}\) at \(65.0^{\circ} \mathrm{C}\) and \(99.2 \mathrm{kPa}\). When the sample is burned in excess oxygen, \(2.4267 \mathrm{g} \mathrm{CO}_{2}\) and \(0.4967 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) are obtained. What is the molecular formula of the hydrocarbon? Write a plausible structural formula for the molecule.
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