# Calculate the mass in grams 2.6 \times 10^{22} SO_2 molecules. Express your answer using two...

## Question:

Calculate the mass in grams {eq}2.6 \times 10^{22} SO_2 {/eq} molecules. Express your answer using two significant figures.

## Moles and Mass Relationship:

The mass of a given substance can be calculated if the amount of substance, namely the number of moles, present is known. The mass in grams equals simply the number of moles present times the molar mass of the substance.

Molar mass of {eq}SO_2 {/eq} molecule is given by:

{eq}M_{SO_2} = 32 \ g\mol + 2\times 16 \ g/mol = 64 \ g/mol {/eq}

The amount of sulfur dioxide is given by:

{eq}\nu_{SO_2} = \dfrac {N}{N_A} {/eq}

Here

• {eq}N_A = 6.023 \times 10^{23} \ mol^{-1} {/eq} is the Avogadro number.

The mass of the sulfur dioxide is then:

{eq}m_{SO_2} = \nu_{SO_2} M_{SO_2} {/eq}

Substituting, we obtain:

{eq}m_{SO_2} = \dfrac {N}{N_A} M_{SO_2} {/eq}

Calculation yields:

{eq}m_{SO_2} = \dfrac {2.6\times 10^{22}}{6.023 \times 10^{23} \ mol^{-1}} \cdot 64 \ g/mol \approx 2.76 \ g {/eq}