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Chapter 10: Problem 59

In a "Kipp generator", hydrogen gas is produced when zinc flakes react with hydrochloric acid: $$2 \mathrm{HCl}(a q)+\mathrm{Zn}(s) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)$$ If \(30.0 \mathrm{~mL}\) of wet \(\mathrm{H}_{2}\) is collected over water at \(20^{\circ} \mathrm{C}\) and a barometric pressure of \(101.33 \mathrm{kPa}\), how many grams of \(\mathrm{Zn}\) have been consumed? (The vapor pressure of water is tabulated in Appendix B.)

Short Answer

Expert verified
Approximately 0.0802 grams of zinc have been consumed in the Kipp generator.

Step by step solution

01

Determine the partial pressure of hydrogen gas

To determine the amount of hydrogen gas produced, first find the partial pressure of hydrogen gas. Subtract the vapor pressure of water at 20°C from the given barometric pressure. Partial Pressure of H₂ (P_H₂) = Barometric Pressure - Vapor Pressure of Water At 20°C, the vapor pressure of water can be found using the tabulated data in Appendix B, which states that it's 2.34 kPa. So: P_H₂ = 101.33 kPa - 2.34 kPa P_H₂ = 98.99 kPa
02

Calculate the moles of hydrogen gas produced

Now that we have the partial pressure of hydrogen gas, we can use the Ideal Gas Law to find the moles of hydrogen gas produced. The Ideal Gas Law is given by: PV = nRT Where P is the pressure (in kPa), V is the volume (in L), n is the number of moles, R is the ideal gas constant (8.314 J/(mol·K)), and T is the temperature (in K). We need to convert the given volume and temperature to appropriate units. Volume of H₂: 30.0 mL = 0.030 L Temperature: 20°C = 293.15 K Rearrange the Ideal Gas Law to solve for n: n = PV/RT Plug in the values: n = (98.99 kPa)(0.030 L) / (8.314 J/(mol·K))(293.15 K) n = 0.001228 mol We have approximately 0.001228 moles of hydrogen gas.
03

Determine the amount of zinc consumed

Now we will use the stoichiometry of the reaction to determine the amount of zinc consumed. The balanced chemical equation is: 2 HCl(aq) + Zn(s) → ZnCl₂(aq) + H₂(g) From the stoichiometry, we can see that 1 mole of H₂ is produced for 1 mole of Zn consumed. Therefore, the moles of Zn consumed are equal to the moles of H₂ produced. Moles of Zn consumed = Moles of H₂ produced = 0.001228 mol
04

Convert moles of zinc to grams

Finally, convert the moles of zinc consumed to grams using the molar mass of zinc, which is approximately 65.38 g/mol. Grams of Zn consumed = Moles of Zn consumed × Molar mass of Zn Grams of Zn consumed = 0.001228 mol × 65.38 g/mol Grams of Zn consumed ≈ 0.0802 g Therefore, approximately 0.0802 grams of zinc have been consumed.

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Most popular questions from this chapter

A glass vessel fitted with a stopcock valve has a mass of $337.428 \mathrm{~g}\( when evacuated. When filled with \)\mathrm{Ar}$, it has a mass of \(339.854 \mathrm{~g}\). When evacuated and refilled with a mixture of Ne and Ar, under the same conditions of temperature and pressure, it has a mass of \(339.076 \mathrm{~g} .\) What is the mole percent of Ne in the gas mixture?

Calculate the pressure that \(\mathrm{CCl}_{4}\) will exert at $80^{\circ} \mathrm{C}\( if 1.00 mol occupies \)33.3 \mathrm{~L}$, assuming that (a) \(\mathrm{CCl}_{4}\) obeys the ideal-gas equation; (b) \(\mathrm{CCl}_{4}\) obeys the van der Waals equation. (Values for the van der Waals constants are given in Table \(10.3 .\) ) (c) Which would you expect to deviate more from ideal behavior under these conditions, \(\mathrm{Cl}_{2}\) or \(\mathrm{CCl}_{4} ?\) Explain.

(a) If the pressure exerted by ozone, \(\mathrm{O}_{3}\), in the stratosphere is \(304 \mathrm{~Pa}\) and the temperature is \(250 \mathrm{~K}\), how many ozone molecules are in a liter? (b) Carbon dioxide makes up approximately \(0.04 \%\) of Earth's atmosphere. If you collect a 2.0-L sample from the atmosphere at sea level \((101.33 \mathrm{kPa})\) on a warm day $\left(27^{\circ} \mathrm{C}\right)\(, how many \)\mathrm{CO}_{2}$ molecules are in your sample?

The temperature of a \(5.00-\mathrm{L}\) container of \(\mathrm{N}_{2}\) gas is increased from \(20^{\circ} \mathrm{C}\) to \(250^{\circ} \mathrm{C}\). If the volume is held constant, predict qualitatively how this change affects the following: (a) the average kinetic energy of the molecules; (b) the rootmean- square speed of the molecules; (c) the strength of the impact of an average molecule with the container walls; \(\mathbf{d}\) ) the total number of collisions of molecules with walls per second.

A 6.0-L tank is filled with helium gas at a pressure of 2 MPa. How many balloons (each \(2.00 \mathrm{~L}\) ) can be inflated to a pressure of $101.3 \mathrm{kPa}$, assuming that the temperature remains constant and that the tank cannot be emptied below \(101.3 \mathrm{kPa}\) ?
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