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Chapter 3: Problem 93

The density of a mixture of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and water is 1.78 g/mL. The percent composition of the mixture is to be determined by converting \(\mathrm{H}_{2} \mathrm{SO}_{4}\) to \(\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) If \(32.0 \mathrm{mL}\) of the mixture gives \(65.2 \mathrm{g}\left(\mathrm{NH}_{4}\right)_{2} \mathrm{SO}_{4}\) then what is the percent composition of the mixture?

Short Answer

Expert verified
The percent composition of sulfuric acid in the mixture is calculated to be the ratio of the mass of the sulfuric acid to the total mass of the mixture, each calculated in their respective steps, and multiplied by 100.

Step by step solution

01

Calculate Mass of Sulfuric Acid from Mass of Ammonium Sulfate

Given that 65.2g of \((\mathrm{NH}_{4})_{2} \mathrm{SO}_{4}\) is obtained from the mixture, we can calculate the mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) from its molar mass and the molar mass of \((\mathrm{NH}_{4})_{2} \mathrm{SO}_{4}\). \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and \((\mathrm{NH}_{4})_{2} \mathrm{SO}_{4}\) are equivalent in terms of moles of sulfur, as each molecule contains one atom of sulfur. Therefore, \(\mathrm{H}_{2} \mathrm{SO}_{4}\) (98.08 g/mol) : \((\mathrm{NH}_{4})_{2} \mathrm{SO}_{4}\) (132.14 g/mol) = 65.2g : x. Solve the proportion for \(x\), which is the mass of sulfuric acid.
02

Calculate Total Mass of Mixture

Using the density of the mixture (1.78 g/mL) and the volume of the mixture (32.0 mL), we can calculate the total mass of the mixture. Multiplying the density by the volume will give the mass in grams.
03

Calculate Percent Composition

Finally, the percent composition of sulfuric acid in the mixture can be calculated by dividing the mass of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) (calculated in step 1) by the total mass of the mixture (calculated in step 2) and then multiplying by 100 to convert it to percentage.

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The formula for calcium chlorite is (a) \(\mathrm{CaClO}_{2}\) (b) \(\mathrm{Ca}\left(\mathrm{ClO}_{2}\right)_{2} ;(\mathrm{c}) \mathrm{CaClO}_{3} ;(\mathrm{d}) \mathrm{Ca}\left(\mathrm{ClO}_{4}\right)_{2}\)

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