How many molecules of sulfur trioxide (SO_3) are present in a 78.0 g sample?

• A. 7.80 × 10^{22} molecules
• B. 5.87 × 10^{23} molecules
• C. 1.56 × 10^{23} molecules
• D. 2.35 × 10^{24} molecules

Answer: (B)

Verified step by step guidance

1. Determine the molar mass of sulfur trioxide (SO\_3) by adding the atomic masses of sulfur (S) and oxygen (O). The atomic mass of sulfur is approximately 32.07 g/mol, and oxygen is approximately 16.00 g/mol. So, calculate the molar mass as: \(M = 32.07 + 3 \times 16.00\) g/mol.
2. Calculate the number of moles of SO\_3 in the 78.0 g sample using the formula: \(n = \frac{\text{mass}}{\text{molar mass}} = \frac{78.0}{M}\), where \(M\) is the molar mass found in step 1.
3. Use Avogadro's number, which is \$6.022 \times 10^{23}\( molecules per mole, to convert moles of SO\_3 to molecules. The formula is: \)\text{number of molecules} = n \times 6.022 \times 10^{23}$.
4. Substitute the value of \(n\) from step 2 into the equation in step 3 to find the total number of molecules in the 78.0 g sample.
5. Compare your calculated number of molecules with the given options to identify the correct answer.