Textbook Question
What is the pH of the solution in the cathode compartment of the following cell if the measured cell potential at 25 °C is 0.58 V? (Refer to Appendix B for standard reduction potentials.) (a) 8.0(b) 4.5(c) 2.2(d) 3.0
Ch.19 - Electrochemistry
Chapter 19, Problem 15
Chlorine can be prepared in the laboratory by the reaction of hydrochloric acid and potassium permanganate. (c) How many liters of Cl₂ at 1.0 atm and 25 °C will result from the reaction of 179 g KMnO₄ with an excess of HCl?
Verified step by step guidance1
Step 1: Write the balanced chemical equation for the reaction between potassium permanganate (KMnO₄) and hydrochloric acid (HCl) to produce chlorine gas (Cl₂). The balanced equation is: 2 KMnO₄ + 16 HCl → 2 MnCl₂ + 5 Cl₂ + 2 KCl + 8 H₂O.
Step 2: Calculate the molar mass of KMnO₄. The molar mass is the sum of the atomic masses of all atoms in the formula: K (39.10 g/mol) + Mn (54.94 g/mol) + 4 O (4 x 16.00 g/mol) = 158.04 g/mol.
Step 3: Determine the number of moles of KMnO₄ used in the reaction. Use the formula: moles = mass (g) / molar mass (g/mol). Substitute the given mass of KMnO₄ (179 g) and the molar mass calculated in Step 2.
Step 4: Use stoichiometry to find the moles of Cl₂ produced. According to the balanced equation, 2 moles of KMnO₄ produce 5 moles of Cl₂. Use the mole ratio from the balanced equation to convert moles of KMnO₄ to moles of Cl₂.
Step 5: Use the ideal gas law to calculate the volume of Cl₂ gas produced at 1.0 atm and 25 °C. The ideal gas law is PV = nRT, where P is pressure, V is volume, n is moles, R is the ideal gas constant (0.0821 L·atm/mol·K), and T is temperature in Kelvin. Convert 25 °C to Kelvin and solve for V.
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Stoichiometry
Stoichiometry is the calculation of reactants and products in chemical reactions. It involves using balanced chemical equations to determine the proportions of substances consumed and produced. In this case, understanding the stoichiometric coefficients from the reaction between KMnO₄ and HCl is essential to find the amount of Cl₂ generated.
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Ideal Gas Law
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. This law is crucial for converting the amount of Cl₂ produced from moles to liters under specified conditions (1.0 atm and 25 °C). Knowing how to manipulate this equation allows for the calculation of gas volumes in chemical reactions.
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Molar Mass
Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For KMnO₄, calculating its molar mass is necessary to convert the given mass (179 g) into moles. This conversion is a fundamental step in stoichiometric calculations, enabling the determination of how many moles of Cl₂ can be produced from the reaction.
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Related Practice
Textbook Question
What are the products of the overall reaction in the elec-trolysis of an aqueous solution of sodium hydroxide? (Refer to Table 19.1 for standard reduction potentials.)(a) Na(s) and O2(g)(b) H2(g) and O2(g)(c) Na(s) and H2(g) (d) Na(s) and H2O2(aq)
Textbook Question
How are standard reduction potentials defined?
Textbook Question
The silver oxide–zinc battery used in watches delivers a voltage of 1.60 V. Calculate the free-energy change (in kilo-joules) for the cell reaction
Textbook Question
Calculate the standard cell potential and the standard free-energy change (in kilojoules) for the reaction below. (See Appendix D for standard reduction potentials.) <QUESTION REFERENCES APPENDIX D>