QQuestionChemistry
QuestionChemistry
The molar mass of silver $(\mathrm{Ag})$ is $107.87 \mathrm{~g} / \mathrm{mol}$.
Calculate the mass in grams of a sample of Ag containing $1.97 \times 10^{22}$ atoms. Write your answer using three significant figures.
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Answer
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Step 1:: Write down the relationship between the number of atoms, the molar mass, and the mass of a substance.
where $m$ is the mass of the sample, $N$ is the number of atoms in the sample, $M$ is the molar mass of the substance, and $N_A$ is Avogadro's number, which is approximately $6.022 \times 10^{23} \text{ atoms/mol}$.
The number of atoms in a sample is related to the mass of the sample through the molar mass of the substance. This relationship is given by the following equation:
Step 2:: Plug in the given values into the equation.
m = (1.97 \times 10^{22}) \text{ atoms} \times \frac{107.87 \text{ g/mol}}{6.022 \times 10^{23} \text{ atoms/mol}}
Plug these values into the equation:
Step 3:: Perform the calculation.
2.134 \times 10^{24} \text{ g} \div 6.022 \times 10^{23} \text{ atoms/mol} = 35.43 \text{ g}
First, calculate the numerator of the fraction: Next, divide this value by Avogadro's number:
Step 4:: Round the answer to three significant figures.
Final Answer
is $35.4 \text{ g}$.
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