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Chapter 3: Problem 188

A 1.500 -g sample of a mixture containing only \(\mathrm{Cu}_{2} \mathrm{O}\) and CuO was treated with hydrogen to produce 1.252 \(\mathrm{g}\) of pure cupper metal. Calculate the mass percent of \(\mathrm{Cu}_{2} \mathrm{O}\) in the original mixture.

Short Answer

Expert verified
The mass percent of Cu2O in the original 1.500 g mixture of Cu2O and CuO is approximately 77.3%.

Step by step solution

01

Calculate moles of produced copper

To determine the moles of copper produced, we can use the equation: moles of copper = mass of copper / molar mass of copper The atomic mass of copper is 63.54 g/mol. Thus, we can calculate the moles of copper produced as follows: moles of copper = 1.252 g / (63.54 g/mol) = 0.0197 mol Now, we have found the moles of produced copper, which is 0.0197 mol.
02

Calculate moles of Cu2O and CuO in the original mixture

Since the produced copper comes from both the Cu2O and CuO in the original mixture and the mixture contains only these two compounds, their moles can be determined as follows: From Cu2O: moles of Cu = 2 × moles of Cu2O moles of Cu2O = (moles of Cu) / 2 From CuO: moles of Cu = moles of CuO Let x be the moles of Cu2O and y be the moles of CuO. Then, we can write an equation based on the moles of copper produced: 0.0197 = (x / 2) + y (1)
03

Calculate the mass of the original Cu2O and CuO

To calculate the mass of the original Cu2O and CuO, we can use the following equations: mass of Cu2O = moles of Cu2O × molar mass of Cu2O mass of CuO = moles of CuO × molar mass of CuO The molar mass of Cu2O is (2 * 63.54) + 16 = 143.08 g/mol, and the molar mass of CuO is 63.54 + 16 = 79.54 g/mol. Since the total mass of the original mixture is given to be 1.500 g, we can write the second equation based on the mass: 143.08x + 79.54y = 1.500 (2)
04

Solve the system of equations for x and y

Now, we solve the system of equations (1) and (2) to find the moles of Cu2O and CuO in the original mixture. Multiply equation (1), with a factor two: 0.0394 = x + 2y (1b) Express y from equation (1b): y = (0.0394 - x) / 2 Now substitute this expression of y into equation (2) and solve for x: 143.08x + 79.54(0.0394 - x) = 1.500 x ≈ 0.00811 Now, substitute the value of x back into the equation for y: y = (0.0394 - 0.00811) / 2 y ≈ 0.0157 We found that the moles of Cu2O and CuO in the original mixture are approximately 0.00811 mol and 0.0157 mol, respectively.
05

Calculate the mass percent of Cu2O in the original mixture

Now, we can calculate the mass percent of Cu2O in the original mixture using the following equation: mass percent of Cu2O = (mass of Cu2O / total mass of the original mixture) × 100% First, calculate the mass of Cu2O: mass of Cu2O = 0.00811 mol × 143.08 g/mol = 1.159 g Now, calculate the mass percent of Cu2O: mass percent of Cu2O = (1.159 g / 1.500 g) × 100% ≈ 77.3% The mass percent of Cu2O in the original mixture is approximately 77.3%.

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