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Chapter 4: Problem 116

Under appropriate conditions, copper sulfate, potassium chromate, and water react to form a product containing \(\mathrm{Cu}^{2+},\) \(\mathrm{CrO}_{4}{^2}{^-},\) and \(\mathrm{OH}^{-}\) ions. Analysis of the compound yields \(48.7 \% \mathrm{Cu}^{2+}, 35.6 \% \mathrm{CrO}_{4}{^2}{-},\) and \(15.7 \% \mathrm{OH}^{-}\). (a) Determine the empirical formula of the compound. (b) Write a plausible equation for the reaction.

Short Answer

Expert verified
The empirical formula of the compound in the given conditions is \(\mathrm{Cu}_{4}( \mathrm{CrO}_{4}) \mathrm{OH}_{5}\). The plausible reaction equation is \(\mathrm{CuSO}_{4} + 2 \mathrm{K}_{2} \mathrm{CrO}_{4} + 5 \mathrm{H}_{2} \mathrm{O} \rightarrow 4\mathrm{Cu}_{4}( \mathrm{CrO}_{4} )\mathrm{OH}_{5} + \mathrm{K}_{2} \mathrm{SO}_{4}\).

Step by step solution

01

Determine molar ratios

To determine the empirical formula of the compound, assume a 100 g sample of the compound. This allows us to treat the percentage composition as grams. This means that we have 48.7 g of \(\mathrm{Cu}^{2+}\), 35.6 g of \(\mathrm{CrO}_{4}{^2}{^-}\), and 15.7 g of \(\mathrm{OH}^{-}\). Then, convert this mass into moles by dividing by the molar mass. For \(\mathrm{Cu}^{2+}\), this gives a value of \(48.7 / 63.55 \approx 0.766\) mol. For \(\mathrm{CrO}_{4}{^2}{^-}\), this gives a value of \(35.6 / 194.19 \approx 0.183\) mol. For \(\mathrm{OH}^{-}\), this gives a value of \(15.7 / 17.01 \approx 0.923\) mol.
02

Calculate the empirical formula

The empirical formula is given by the ratios of these moles. To get the smallest whole numbers, divide all the mole values by the smallest of the three. In this case, the smallest value is that of \(\mathrm{CrO}_{4}{^2}{^-}\), which gives ratios of 4 for \(\mathrm{Cu}^{2+}\), 1 for \(\mathrm{CrO}_{4}{^2}{^-}\), and 5 for \(\mathrm{OH}^{-}\). Thus, the empirical formula of the compound is \(\mathrm{Cu}_{4}( \mathrm{CrO}_{4}) \mathrm{OH}_{5}\).
03

Write the reaction equation

Now, using the reactants copper sulfate, potassium chromate, and water, and under appropriate conditions, we may suggest a plausible equation for the reaction. With the empirical formula, \(\mathrm{CuSO}_{4} + 2 \mathrm{K}_{2} \mathrm{CrO}_{4} + 5 \mathrm{H}_{2} \mathrm{O} \rightarrow 4\mathrm{Cu}_{4}( \mathrm{CrO}_{4} )\mathrm{OH}_{5} + \mathrm{K}_{2} \mathrm{SO}_{4}\) is plausible, having in mind that ions in water solution are present.

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Most popular questions from this chapter

Which of the following is a \(0.500 \mathrm{M} \mathrm{KCl}\) solution? (a) \(0.500 \mathrm{g} \mathrm{KCl} / \mathrm{mL}\) solution; (b) \(36.0 \mathrm{g} \mathrm{KCl} / \mathrm{L}\) solu- tion; (c) 7.46 mg KCl/mL solution; (d) 373 g KCl in 10.00 L solution

What are the molarities of the following solutes when dissolved in water? (a) \(2.92 \mathrm{mol} \mathrm{CH}_{3} \mathrm{OH}\) in 7.16 L of solution (b) \(7.69 \mathrm{mmol} \mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{OH}\) in \(50.00 \mathrm{mL}\) of solution (c) \(25.2 \mathrm{g} \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}\) in \(275 \mathrm{mL}\) of solution

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