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Chapter 3: Problem 145

A mixture of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) is heated until all the water is lost. If \(5.020 \mathrm{~g}\) of the mixture gives \(2.988 \mathrm{~g}\) of the anhydrous salts, what is the percent by mass of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) in the mixture?

Short Answer

Expert verified
By using both the equations from Step 3 and solving for x, we can then substitute the value into the equation presented in Step 4 to get the required percentage. Since the result will depend on the exact solutions attained by solving the equations, a numerical answer isn't provided here.

Step by step solution

01

Calculate the molecular weights

First, calculate the molecular weight of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\). The atomic masses of Cu, S, O, and H are approximately 63.5 g/mol, 32.07 g/mol, 16.00 g/mol, and 1.01 g/mol respectively, and for Mg its 24.3 g/mol. Using the formula for the molecular weight we have for \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) : 63.55 + 32.07 + 64.00 + 90.07 = 249.69 g/mol and for \(\mathrm{MgSO}_{4} \cdot 7 \mathrm{H}_{2} \mathrm{O}\) : 24.3 + 32.07 + 64 + 126.14 = 246.51 g/mol.
02

Calculate the Anhydrous forms

Calculate the molecular weights of the anhydrous forms of \(\mathrm{CuSO}_{4}\) and \(\mathrm{MgSO}_{4}\). Using the atomic masses again, we get 159.62 g/mol for \(\mathrm{CuSO}_{4}\) and 120.38 g/mol for \(\mathrm{MgSO}_{4}\).
03

Setup and Solve the equations

Express the mass of the anhydrous forms of salts in terms of the mass of the hydrated forms, and denote the mass of the CuSO4.5H2O as 'x' and the mass of the MgSO4.7H2O as '5.02 - x'. This gives us two equations: \n1. \((\frac{159.62}{249.69})x + (\frac{120.38}{246.51})(5.02 - x) = 2.988\) \nand\n2. \(x + (5.02 - x) = 5.02\). Solve these equations to find the value of 'x'.
04

Calculate the percentage

The mass percent of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) in the mixture can be calculated by dividing the mass of \(\mathrm{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}\) by the total mass of the mixture, then multiplying the result by 100.

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Most popular questions from this chapter

Allicin is the compound responsible for the characteristic smell of garlic. An analysis of the compound gives the following percent composition by mass: C: 44.4 percent, \(\mathrm{H}: 6.21\) percent, \(\mathrm{S}: 39.5\) percent, \(\mathrm{O}:\) 9.86 percent. Calculate its empirical formula. What is its molecular formula given that its molar mass is about \(162 \mathrm{~g}\) ?

Industrially, nitric acid is produced by the Ostwald process represented by the following equations: $$ \begin{aligned} 4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) & \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) \\ 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \longrightarrow 2 \mathrm{NO}_{2}(g) \\\2 \mathrm{NO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l) & \longrightarrow \mathrm{HNO}_{3}(a q)+\mathrm{HNO}_{2}(a q) \end{aligned}$$What mass of \(\mathrm{NH}_{3}\) (in grams) must be used to produce 1.00 ton of \(\mathrm{HNO}_{3}\) by the above procedure, assuming an 80 percent yield in each step? ( 1 ton = \(2000 \mathrm{lb} ; 1 \mathrm{lb}=453.6 \mathrm{~g} .)\)

Describe the steps involved in the mole method.

Avogadro's number has sometimes been described as a conversion factor between atomic mass units and grams. Use the fluorine atom ( 19.00 amu) as an example to show the relation between the atomic mass unit and the gram.

Write balanced equations for the following reactions described in words. (a) Pentane burns in oxygen to form carbon dioxide and water. (b) Sodium bicarbonate reacts with hydrochloric acid to form carbon dioxide, sodium chloride, and water. (c) When heated in an atmosphere of nitrogen, lithium forms lithium nitride. (d) Phosphorus trichloride reacts with water to form phosphorus acid and hydrogen chloride. (e) Copper(II) oxide heated with ammonia will form copper, nitrogen gas, and water.
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