The molar mass of bismuth (Bi) is 208.98 g/mol. Calculate the mass in grams of a sample of Bi containing 7.35 × 10^23 atoms. Write your answer using three significant figures. (for this problem, do not use scientific notation)
The Correct Answer and Explanation is:
To calculate the mass in grams of a sample containing 7.35×10237.35 \times 10^{23}7.35×1023 atoms of bismuth (Bi), we need to use the concept of moles and the molar mass.
Step 1: Use Avogadro’s number
Avogadro’s number tells us that one mole of any substance contains 6.022×10236.022 \times 10^{23}6.022×1023 particles (atoms, molecules, etc.). Therefore, we can calculate the number of moles of bismuth atoms in the given sample.
The number of moles (nnn) is given by the formula: n=Number of atomsAvogadro’s number=7.35×10236.022×1023n = \frac{\text{Number of atoms}}{\text{Avogadro’s number}} = \frac{7.35 \times 10^{23}}{6.022 \times 10^{23}}n=Avogadro’s numberNumber of atoms=6.022×10237.35×1023
This simplifies to: n=1.22 molesn = 1.22 \text{ moles}n=1.22 moles
Step 2: Calculate the mass using the molar mass
Now, we use the molar mass of bismuth to find the mass of the sample. The molar mass of bismuth (Bi) is 208.98 g/mol208.98 \, \text{g/mol}208.98g/mol. The formula to calculate the mass (mmm) is: m=n×Molar massm = n \times \text{Molar mass}m=n×Molar mass
Substituting the values we have: m=1.22 mol×208.98 g/molm = 1.22 \, \text{mol} \times 208.98 \, \text{g/mol}m=1.22mol×208.98g/mol m=254.97 gm = 254.97 \, \text{g}m=254.97g
Step 3: Round to three significant figures
Since the problem asks for the answer in three significant figures, we round the result: m=255 gm = 255 \, \text{g}m=255g
Final Answer:
The mass of the bismuth sample is 255 grams.
