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Chapter 5: Problem 76

Ethene is converted to ethane by the reaction $$ \mathrm{C}_{2} \mathrm{H}_{4}(g)+\mathrm{H}_{2}(g) \stackrel{\text { Catalyst }}{\longrightarrow} \mathrm{C}_{2} \mathrm{H}_{6}(g) $$ \(\mathrm{C}_{2} \mathrm{H}_{4}\) flows into a catalytic reactor at \(25.0 \mathrm{~atm}\) and \(300 .{ }^{\circ} \mathrm{C}\) with a flow rate of \(1000 . \mathrm{L} / \mathrm{min}\). Hydrogen at \(25.0 \mathrm{~atm}\) and \(300 .{ }^{\circ} \mathrm{C}\) flows into the reactor at a flow rate of \(1500 . \mathrm{L} / \mathrm{min}\). If \(15.0 \mathrm{~kg}\) \(\mathrm{C}_{2} \mathrm{H}_{6}\) is collected per minute, what is the percent yield of the reaction?

Short Answer

Expert verified
Percent Yield = \(\frac{15,000}{(25,000 / 47.08) * 30.07} * 100\) (approximately) ≈ 91.3%

Step by step solution

01

Calculate the moles of Ethene and Hydrogen

First, we need to calculate the moles of Ethene and Hydrogen that are flowing into the reactor. We will use the Ideal Gas Equation as following: \(PV = nRT\) Where: P = Pressure V = Volume n = moles R = Ideal Gas Constant (0.0821 L atm / K mol) T = Temperature in Kelvin First, convert the temperature from Celsius to Kelvin: \(T = 300 + 273.15 = 573.15 K\) Now, calculate the moles of Ethene and Hydrogen: For Ethene: \(P_V = n_ER_T\) \(25.0 atm * 1000 L/min = n_E * 0.0821 * 573.15 K\) \(n_E = \frac{25,000}{47.08}\) moles/min (approximately) For Hydrogen: \(P_H = n_HR_H\) \(25.0 atm * 1500 L/min = n_H * 0.0821 * 573.15 K\) \(n_H = \frac{37,500}{47.08}\) moles/min (approximately)
02

Determine the limiting reactant

Since the reaction has a 1:1 mole ratio between Ethene (C₂H₄) and Hydrogen (H₂), we can compare their moles to determine the limiting reactant: The ratio of moles between Ethene and Hydrogen is: \(\frac{n_E}{n_H} = \frac{25,000 / 47.08}{37,500 / 47.08} = \frac{25,000}{37,500}\) (approximately) Since the ratio is less than 1, Ethene (C₂H₄) is the limiting reactant.
03

Calculate the theoretical yield

Using the limiting reactant, we can calculate the theoretical yield of Ethane (C₂H₆). According to the balanced chemical equation, 1 mol of Ethene (C₂H₄) produces 1 mol of Ethane (C₂H₆). Therefore, the theoretical yield will be the same as the moles of Ethene: n(C₂H₆) = n(C₂H₄) = 25,000 / 47.08 (approximately) moles/min Now convert moles of Ethane (C₂H₆) to mass using its molar mass (30.07 g/mol): mass(C₂H₆) = 25,000 / 47.08 * 30.07 g/mol (approximately)
04

Calculate the percent yield

Now that we have the theoretical yield, we can use the actual yield given (15 kg/min) to find the percent yield: Percent Yield = \(\frac{Actual Yield}{Theoretical Yield} * 100\) Percent Yield = \(\frac{15,000 g/min}{25,000 / 47.08 * 30.07 g/mol} * 100\) (approximately) Calculate the percent yield and that will be our answer.

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Most popular questions from this chapter

In 1897 the Swedish explorer Andreé tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is $$ \mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{FeSO}_{4}(a q)+\mathrm{H}_{2}(g) $$ The volume of the balloon was \(4800 \mathrm{~m}^{3}\) and the loss of hydrogen gas during filling was estimated at \(20 . \%\). What mass of iron splints and \(98 \%\) (by mass) \(\mathrm{H}_{2} \mathrm{SO}_{4}\) were needed to ensure the complete filling of the balloon? Assume a temperature of \(0^{\circ} \mathrm{C}\), a pressure of \(1.0\) atm during filling, and \(100 \%\) yield.

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Consider two gases, A and B, each in a 1.0-L container with both gases at the same temperature and pressure. The mass of gas \(\mathrm{A}\) in the container is \(0.34 \mathrm{~g}\) and the mass of gas \(\mathrm{B}\) in the container is \(0.48 \mathrm{~g}\). a. Which gas sample has the most molecules present? Explain. b. Which gas sample has the largest average kinetic energy? Explain. c. Which gas sample has the fastest average velocity? Explain. d. How can the pressure in the two containers be equal to each other since the larger gas B molecules collide with the container walls more forcefully?

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