Question
Determine if the statement is True or False. The molar mass of ammonium acetate is 77.083 g/mol. A student uses 0.100 mol of ammonium acetate in a chemical reaction. The student claims that the reaction uses (0.100 mol)(77.083 gmol) = 7.71 g of ammonium acetate, which has (7.71)(6.022×1023) = 4.64×1024 molecules. Did the student determine the correct number of molecules of ammonium acetate used in the reaction? (2 points) Responses The student calculated the correct number of molecules of ammonium acetate. The student calculated the correct number of molecules of ammonium acetate. The student miscalculated the number of molecules of ammonium acetate. The student miscalculated the number of molecules of ammonium acetate. Skip to navigation
Answers
GPT-4o mini
To determine whether the student's calculations are correct, let's go through them step by step.
1. **Calculating mass from moles and molar mass:**
The student uses the formula:
\[
\text{mass} = \text{moles} \times \text{molar mass}
\]
Given that the student uses 0.100 mol of ammonium acetate and the molar mass is 77.083 g/mol, the calculation should be:
\[
\text{mass} = 0.100 \, \text{mol} \times 77.083 \, \text{g/mol} = 7.7083 \, \text{g} \approx 7.71 \, \text{g}
\]
This calculation is correct.
2. **Calculating number of molecules:**
The number of molecules can be calculated using Avogadro's number:
\[
\text{number of molecules} = \text{moles} \times N_A
\]
Here \(N_A = 6.022 \times 10^{23} \, \text{molecules/mol}\):
\[
\text{number of molecules} = 0.100 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}
\]
Calculating this gives:
\[
\text{number of molecules} = 0.100 \times 6.022 \times 10^{23} = 6.022 \times 10^{22} \, \text{molecules}
\]
3. **Comparison with the student's number:**
The student claims the number of molecules used is \(4.64 \times 10^{24}\), which is incorrect.
Thus, the student's result for the number of molecules of ammonium acetate used in the reaction is incorrect.
**Final answer:** The student miscalculated the number of molecules of ammonium acetate.
1. **Calculating mass from moles and molar mass:**
The student uses the formula:
\[
\text{mass} = \text{moles} \times \text{molar mass}
\]
Given that the student uses 0.100 mol of ammonium acetate and the molar mass is 77.083 g/mol, the calculation should be:
\[
\text{mass} = 0.100 \, \text{mol} \times 77.083 \, \text{g/mol} = 7.7083 \, \text{g} \approx 7.71 \, \text{g}
\]
This calculation is correct.
2. **Calculating number of molecules:**
The number of molecules can be calculated using Avogadro's number:
\[
\text{number of molecules} = \text{moles} \times N_A
\]
Here \(N_A = 6.022 \times 10^{23} \, \text{molecules/mol}\):
\[
\text{number of molecules} = 0.100 \, \text{mol} \times 6.022 \times 10^{23} \, \text{molecules/mol}
\]
Calculating this gives:
\[
\text{number of molecules} = 0.100 \times 6.022 \times 10^{23} = 6.022 \times 10^{22} \, \text{molecules}
\]
3. **Comparison with the student's number:**
The student claims the number of molecules used is \(4.64 \times 10^{24}\), which is incorrect.
Thus, the student's result for the number of molecules of ammonium acetate used in the reaction is incorrect.
**Final answer:** The student miscalculated the number of molecules of ammonium acetate.