Q1. A particular silver solder is to have the atom ratio of 5.00 Ag : 4.00 Cu : 1.00 Zn. What masses of the three metals must be melted together to prepare 1.00 kg of the solder?

Background

Topic: Stoichiometry and Mass Calculations from Atomic Ratios

This question tests your ability to convert atomic ratios into mass ratios, and then determine the mass of each component in a mixture of known total mass.

Key Terms and Formulas

• Atomic ratio: The ratio of the number of atoms of each element in the mixture.

• Molar mass: The mass of one mole of a substance (g/mol).

• Total mass: The sum of the masses of all components.

Key formula:

Step-by-Step Guidance

1. Let the number of "units" in the mixture be based on the atomic ratio: 5 Ag, 4 Cu, 1 Zn per unit. Calculate the total number of atoms per unit (5 + 4 + 1 = 10 atoms per unit).

2. Let x be the number of such units in the 1.00 kg (1000 g) sample. Express the number of moles of each metal in terms of x.

3. Write the mass of each metal as , using the molar masses: Ag (107.87 g/mol), Cu (63.55 g/mol), Zn (65.38 g/mol).

4. Set up an equation for the total mass: .

5. Plug in the expressions for each mass in terms of x and solve for x. Once you have x, you can find the mass of each metal.

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Q2. Two compounds made up of Cl and X have molecular masses and % Cl (by mass) as follows: 137 u, 77.5% Cl; 208 u, 85.1% Cl. What is element X? What is the formula for each compound?

Background

Topic: Empirical and Molecular Formula Determination

This question tests your ability to use percent composition and molar mass to deduce the identity of an unknown element and the formulas of compounds.

Key Terms and Formulas

• Percent composition: The percentage by mass of each element in a compound.

• Molecular mass: The sum of the atomic masses of all atoms in a molecule.

• Empirical formula: The simplest whole-number ratio of atoms in a compound.

Key formula:

Step-by-Step Guidance

1. For each compound, calculate the mass of Cl in one mole using the given percentage and molecular mass.

2. Divide the mass of Cl by the atomic mass of Cl (35.45 u) to find the number of Cl atoms per molecule.

3. Subtract the mass of Cl from the total molecular mass to find the mass of X in each compound.

4. Divide the mass of X by the atomic mass of X to find the number of X atoms per molecule.

5. Compare the results for both compounds to deduce the atomic mass of X and thus its identity. Use this to write the formulas.

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Q3. Dimethylhydrazine is a carbon-hydrogen-nitrogen compound used in rocket fuels. When burned in excess oxygen, a 0.312 g sample yields 0.458 g CO2 and 0.374 g H2O. In a separate experiment, the nitrogen content of a 0.486 g sample is converted to 0.226 g N2. What is the empirical formula of dimethylhydrazine?

Background

Topic: Empirical Formula Determination from Combustion Analysis

This question tests your ability to determine the empirical formula of a compound from combustion data and nitrogen analysis.

Key Terms and Formulas

• Empirical formula: The simplest whole-number ratio of atoms in a compound.

• Combustion analysis: A method to determine the amounts of C and H by measuring CO2 and H2O produced.

• Mole calculation:

Key molar masses: CO2 (44.01 g/mol), H2O (18.02 g/mol), N2 (28.02 g/mol)

Step-by-Step Guidance

1. Calculate the moles of CO2 and H2O produced from the combustion of 0.312 g sample.

2. From the moles of CO2, determine the moles of C in the original sample. From H2O, determine the moles of H.

3. From the separate experiment, calculate the moles of N2 produced from 0.486 g sample, and thus the moles of N in the original sample.

4. Adjust the moles of C, H, and N to correspond to the same sample size (scale as needed).

5. Divide the moles of each element by the smallest value to get the simplest whole-number ratio for the empirical formula.

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Q4. Azobenzene can be prepared from nitrobenzene by reaction with triethylene glycol in the presence of Zn and KOH. In one reaction, 0.10 L of nitrobenzene (d = 1.20 g/mL) and 0.30 L of triethylene glycol (d = 1.12 g/mL) yields 55. g azobenzene. What are the a) theoretical yield, b) actual yield, and c) percent yield of this reaction?

Background

Topic: Limiting Reactant and Percent Yield Calculations

This question tests your ability to determine the limiting reactant, calculate theoretical yield, and compute percent yield from experimental data.

Key Terms and Formulas

• Limiting reactant: The reactant that is completely consumed first, limiting the amount of product formed.

• Theoretical yield: The maximum amount of product that can be formed from the limiting reactant.

• Percent yield:

Key formula:

Step-by-Step Guidance

1. Calculate the mass of nitrobenzene and triethylene glycol used, using their volumes and densities.

2. Convert the masses to moles using their molar masses (nitrobenzene: 123.11 g/mol, triethylene glycol: 150.17 g/mol).

3. Use the balanced equation to determine the stoichiometric ratio and identify the limiting reactant.

4. Calculate the theoretical yield of azobenzene (molar mass: 182.23 g/mol) based on the limiting reactant.

5. Use the actual yield (55 g) and theoretical yield to calculate the percent yield.

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Q5. Consider the following nuclei: , , , . Determine which nucleus would receive the greatest pairing advantage. Can you use this information to determine which nucleus is the most stable? Explain.

Background

Topic: Nuclear Stability and Pairing Energy

This question tests your understanding of nuclear structure, specifically the effect of proton-proton and neutron-neutron pairing on nuclear stability.

Key Terms and Concepts

• Pairing energy: Extra stability associated with pairs of protons or neutrons.

• Even-even nuclei: Nuclei with even numbers of both protons and neutrons are generally more stable.

• Odd-odd, odd-even, even-odd: Nuclei with odd numbers of protons or neutrons are generally less stable.

Step-by-Step Guidance

1. For each nucleus, determine the number of protons and neutrons.

2. Identify whether the number of protons and neutrons are even or odd for each nucleus.

3. Recall that nuclei with both even protons and even neutrons have the greatest pairing advantage.

4. Compare the nuclei to see which has the greatest pairing advantage based on their evenness/oddness.

5. Consider whether this pairing advantage directly determines which nucleus is the most stable, or if other factors may also play a role.

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Q6. A 25.00 mL sample of HCl(aq) was added to a 0.10000 g sample of CaCO3. All the CaCO3 reacted, leaving some excess HCl(aq). The excess HCl(aq) required 43.82 mL of 0.01185 M Ba(OH)2 to complete the following reaction. What was the molarity of the original HCl(aq)?

Background

Topic: Titration and Back-Titration Calculations

This question tests your ability to use stoichiometry and titration data to determine the concentration of an acid solution.

Key Terms and Formulas

• Molarity (M): Moles of solute per liter of solution.

• Stoichiometry: Using balanced chemical equations to relate amounts of reactants and products.

• Back-titration: Determining the amount of a reactant by titrating the excess after reaction with another substance.

Key formulas:

• Balanced equations:

Step-by-Step Guidance

1. Calculate the moles of Ba(OH)2 used in the titration of the excess HCl.

2. Use the stoichiometry of the reaction to find the moles of excess HCl neutralized by Ba(OH)2.

3. Calculate the moles of HCl that reacted with CaCO3 using the mass of CaCO3 and its reaction stoichiometry.

4. Add the moles of HCl that reacted with CaCO3 and the moles of excess HCl to get the total moles of HCl originally present.

5. Divide the total moles of HCl by the original volume (25.00 mL) to find the molarity.

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Q7. A mixture contains only CuCl2 and FeCl3. A 0.7391 g sample is dissolved and treated with AgNO3(aq), precipitating all the chloride as AgCl. If it takes 86.91 mL of 0.1463 M AgNO3 to precipitate all the chloride, what is the percentage by mass of copper in the mixture?

Background

Topic: Gravimetric Analysis and Stoichiometry

This question tests your ability to use precipitation reactions and stoichiometry to determine the composition of a mixture.

Key Terms and Formulas

• Gravimetric analysis: Determining the amount of an analyte based on the mass of a product.

• Stoichiometry: Relating moles of reactants and products using balanced equations.

• Key reactions:

Key formula:

Step-by-Step Guidance

1. Calculate the moles of AgNO3 used in the reaction.

2. Since each mole of AgNO3 precipitates one mole of Cl-, determine the total moles of Cl- in the sample.

3. Let x = moles of CuCl2 and y = moles of FeCl3. Set up equations relating x and y to the total moles of Cl- and the total mass of the sample.

4. Use the molar masses of CuCl2 and FeCl3 to relate x and y to the total mass (0.7391 g).

5. Solve the system of equations to find the moles (and thus mass) of CuCl2, then calculate the percentage by mass of copper in the mixture.

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Q8. Hydrogen gas reacts with nitrogen gas to form ammonia. A reaction mixture initially contains 3.00 mol H2 and 1.00 mol N2. After the reaction, 0.400 mol N2 remains. Write a balanced chemical equation for the reaction and calculate the final number of moles of H2 and NH3.

Background

Topic: Stoichiometry and Limiting Reactant Calculations

This question tests your ability to use a balanced chemical equation to relate reactants and products, and to calculate the amounts remaining after a reaction.

Key Terms and Formulas

• Balanced equation: Shows the stoichiometric relationship between reactants and products.

• Limiting reactant: The reactant that is completely consumed first.

• Stoichiometric calculations: Use mole ratios from the balanced equation.

Key reaction:

Step-by-Step Guidance

1. Write the balanced chemical equation for the formation of ammonia from hydrogen and nitrogen.

2. Determine how many moles of N2 reacted by subtracting the final amount from the initial amount.

3. Use the stoichiometry of the reaction to calculate the moles of H2 consumed and NH3 produced.

4. Subtract the moles of H2 consumed from the initial amount to find the final moles of H2.

5. Summarize the final moles of H2 and NH3 present after the reaction.

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