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Chapter 3: Problem 75

When potassium chlorate is burned, potassium chloride and oxygen are formed. (a) Write a balanced equation for the reaction. (b) How much potassium chlorate must be burned to produce \(198.5 \mathrm{~g}\) of oxygen? The yield is found to be \(83.2 \%\).

Short Answer

Expert verified
Answer: 609.25 g of potassium chlorate.

Step by step solution

01

Write the balanced equation

First, write down the unbalanced equation for the given reaction: $$ \mathrm{KClO_3} \rightarrow \mathrm{KCl} + \mathrm{O_2} $$ To balance the equation, we need to adjust the coefficients in the reaction to ensure that the number of atoms of each element is the same on both sides. Balanced equation: $$ \mathrm{2KClO_3} \rightarrow \mathrm{2KCl} + \mathrm{3O_2} $$
02

Calculate moles of oxygen

Now that we have a balanced equation, we can calculate the moles of oxygen needed. We are given that we need \(198.5 \mathrm{~g}\) of oxygen and we know the molar mass of oxygen is approximately \(32 \mathrm{~g/mol}\). Number of moles of oxygen = \(\frac{\text{mass}}{\text{molar mass}}\) $$ \frac{198.5 \mathrm{~g}}{32 \mathrm{~g/mol}} = 6.203125 \mathrm{~mol} $$
03

Calculate moles of potassium chlorate

Now we need to find how many moles of potassium chlorate are needed to produce the desired amount of oxygen, according to the balanced equation. From the balanced equation, we can see that 2 moles of potassium chlorate produce 3 moles of oxygen. $$ \frac{\text{moles of potassium chlorate}}{\text{moles of oxygen}} = \frac{2}{3} $$ To calculate the moles of potassium chlorate required, simply multiply the moles of oxygen by the coefficient ratio. $$ \text{moles of potassium chlorate} = 6.203125 \mathrm{~mol} \times \frac{2}{3} = 4.13541667 \mathrm{~mol} $$
04

Calculate grams of potassium chlorate

To find the mass of potassium chlorate required, we need to consider the yield given (83.2%). We will multiply the calculated moles of potassium chlorate by its molar mass and then divide by the yield to obtain the actual amount needed. Molar mass of potassium chlorate: $$ \mathrm{KClO_3} = 39.1 (\mathrm{K}) + 35.5 (\mathrm{Cl}) + 3 \times 16 (\mathrm{O}) = 122.6 \mathrm{~g/mol} $$ Mass of potassium chlorate required (without considering yield): $$ 4.13541667 \mathrm{~mol} \times 122.6 \mathrm{~g/mol} = 507.073100685 \mathrm{~g} $$ Taking into account the yield (83.2%): $$ \frac{507.073100685 \mathrm{~g}}{0.832} = 609.24897156 \mathrm{~g} $$
05

Final answer

Thus, \(609.25 \mathrm{~g}\) (rounded to 2 decimal places) of potassium chlorate must be burned to produce \(198.5 \mathrm{~g}\) of oxygen with a yield of \(83.2 \%\).

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Most popular questions from this chapter

Consider the hypothetical reaction $$ 8 \mathrm{~A}_{2} \mathrm{~B}_{3}(s)+3 \mathrm{X}_{4}(g) \longrightarrow 4 \mathrm{~A}_{4} \mathrm{X}_{3}(s)+12 \mathrm{~B}_{2}(g) $$ When \(10.0 \mathrm{~g}\) of \(\mathrm{A}_{2} \mathrm{~B}_{3}(\mathrm{MM}=255 \mathrm{~g} / \mathrm{mol})\) react with an excess of \(\mathrm{X}_{4}, 4.00 \mathrm{~g}\) of \(\mathrm{A}_{4} \mathrm{X}_{3}\) are produced. (a) How many moles of \(A_{4} X_{3}\) are produced? (b) What is the molar mass of \(\mathrm{A}_{4} \mathrm{X}_{3}\) ?

Perhaps the simplest way to calculate Avogadro's number is to compare the charge on the electron, first determined by Robert Millikan in 1909, with the charge on a mole of electrons, determined electrochemically (Chapter 18). These charges, in coulombs (C), are given in Appendix 1 . Use them to calculate Avogadro's number to five significant figures.

Riboflavin is one of the \(\mathrm{B}\) vitamins. It is also known as vitamin \(\mathrm{B}_{6}\) and is made up of carbon, hydrogen, nitrogen, and oxygen atoms. When \(10.00 \mathrm{~g}\) of vitamin \(\mathrm{B}_{6}\) is burned in oxygen, \(19.88 \mathrm{~g}\) of \(\mathrm{CO}_{2}\) and \(4.79 \mathrm{~g}\) of \(\mathrm{H}_{2} \mathrm{O}\) are obtained. Another experiment shows that vitamin \(\mathrm{B}_{6}\) is made up of \(14.89 \% \mathrm{~N}\). What is the simplest formula for vitamin \(\mathrm{B}_{6}\) ?

Determine the simplest formulas of the following compounds: (a) saccharin, the artificial sweetener, which has the composition \(45.90 \% \mathrm{C}, 2.75 \% \mathrm{H}, 26.20 \% \mathrm{O}, 17.50 \% \mathrm{~S}\), and \(7.65 \% \mathrm{~N}\) (b) allicin, the compound that gives garlic its characteristic odor, which has the composition \(6.21 \% \mathrm{H}, 44.4 \% \mathrm{C}, 9.86 \% \mathrm{O}\), and \(39.51 \% \mathrm{~S}\). (c) sodium thiosulfate, the fixer used in developing photographic film, which has the composition \(30.36 \% \mathrm{O}, 29.08 \% \mathrm{Na}\), and \(40.56 \% \mathrm{~S}\).

Strontium has four isotopes with the following masses: \(83.9134\) amu \((0.56 \%), 85.9094 \mathrm{amu}(9.86 \%), 86.9089 \mathrm{amu}(7.00 \%)\), and \(87.9056(82.58 \%)\) Calculate the atomic mass of strontium.
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