Question

directions: use dimensional analysis to perform the following calculatior include your units, and box your final answers. 1. how many molecules are in 13.5 g of sulfur dioxide, so₂?

Explanation:

Step 1: Calculate molar mass of \(SO_2\)

Molar mass of \(S\) is \(32.07\space g/mol\), molar mass of \(O\) is \(16.00\space g/mol\). For \(SO_2\), molar mass \(M = 32.07 + 2\times16.00 = 64.07\space g/mol\).

Step 2: Convert mass to moles

Use formula \(n=\frac{m}{M}\), where \(m = 13.5\space g\), \(M = 64.07\space g/mol\). So \(n=\frac{13.5\space g}{64.07\space g/mol}\approx0.2107\space mol\).

Step 3: Convert moles to molecules

Use Avogadro's number \(N_A = 6.022\times10^{23}\space molecules/mol\). Number of molecules \(N = n\times N_A = 0.2107\space mol\times6.022\times10^{23}\space molecules/mol\approx1.27\times10^{23}\space molecules\).

Answer:

\(\boxed{1.27\times10^{23}\text{ molecules}}\)