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Chapter 3: Problem 113

Coke is an impure form of carbon that is often used in the industrial production of metals from their oxides. If a sample of coke is \(95 \%\) carbon by mass, determine the mass of coke needed to react completely with \(1.0\) ton of copper(II) oxide. $$ 2 \mathrm{CuO}(s)+\mathrm{C}(s) \longrightarrow 2 \mathrm{Cu}(s)+\mathrm{CO}_{2}(g) $$

Short Answer

Expert verified
To react completely with 1.0 ton of copper(II) oxide, about 79.374 kg of the given coke sample will be needed.

Step by step solution

01

1. Calculate the number of moles of copper(II) oxide in 1 ton

One ton is equal to 1000 kg. Start by converting the given mass of copper(II) oxide to moles. The molar mass of CuO is calculated as \(Cu (63.546g/mol) + O (16g/mol)\), which is 79.546 g/mol. Moles of CuO = \(\frac{Mass_{CuO}}{Molar\_mass_{CuO}}\) Moles of CuO = \(\frac{1000\,\mathrm{kg}}{79.546\,\mathrm{g/mol}} = 12567.312\,\mathrm{moles}\)
02

2. Determine the moles of carbon needed for this reaction

According to the balanced chemical equation: $$ 2 \mathrm{CuO}(s)+\mathrm{C}(s) \longrightarrow 2 \mathrm{Cu}(s)+\mathrm{CO}_{2}(g) $$ 2 moles of CuO react completely with 1 mole of carbon. Find the moles of carbon needed. Moles of C = \(\frac{1}{2} * Moles_{CuO}\) Moles of C = \(\frac{1}{2} * 12567.312 = 6283.656\,\mathrm{moles}\)
03

3. Calculate the mass of carbon required

Now, convert the moles of carbon to mass using the molar mass of carbon (12 g/mol). Mass of C = \(Moles_C * Molar\_mass_C\) Mass of C = \(6283.656 * 12 = 75,403.87\, \mathrm{g}\) or \(75.40387\,\mathrm{kg}\)
04

4. Determine the mass of coke required

Since we know that the coke sample has 95% carbon by mass, we need to find how much coke is necessary to obtain 75.40387 kg of carbon. Let the mass of coke be x. Then, \(95 \%\) of x should equal to the mass of carbon required. Solve for x: \(x * 0.95 = 75.40387\, \mathrm{kg}\) Mass of coke (x) = \(\frac{75.40387}{0.95} = 79.374\, \mathrm{kg}\)
05

Conclusion

To react completely with 1.0 ton of copper(II) oxide, about 79.374 kg of the given coke sample will be needed.

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Most popular questions from this chapter

Arrange the following substances in order of increasing mass percent of carbon. a. caffeine, \(\mathrm{C}_{8} \mathrm{H}_{10} \mathrm{~N}_{4} \mathrm{O}_{2}\) b. sucrose, \(\bar{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\) c. ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\)

Consider a mixture of potassium chloride and potassium nitrate that is \(43.2 \%\) potassium by mass. What is the percent KCl by mass of the original mixture?

Consider samples of phosphine \(\left(\mathrm{PH}_{3}\right.\) ), water \(\left(\mathrm{H}_{2} \mathrm{O}\right)\), hydrogen sulfide \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\), and hydrogen fluoride (HF), each with a mass of \(119 \mathrm{~g}\). Rank the compounds from the least to the greatest number of hydrogen atoms contained in the samples.

Adipic acid is an organic compound composed of \(49.31 \% \mathrm{C}\), \(43.79 \% \mathrm{O}\), and the rest hydrogen. If the molar mass of adipic acid is \(146.1 \mathrm{~g} / \mathrm{mol}\), what are the empirical and molecular formulas for adipic acid?

Ammonia is produced from the reaction of nitrogen and hydrogen according to the following balanced equation: $$ \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g) \longrightarrow 2 \mathrm{NH}_{3}(g) $$ a. What is the maximum mass of ammonia that can be produced from a mixture of \(1.00 \times 10^{3} \mathrm{~g} \mathrm{~N}_{2}\) and \(5.00 \times 10^{2} \mathrm{~g} \mathrm{H}_{2} ?\) b. What mass of which starting material would remain unreacted?
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