Chapter 7: Problem 29

A scientist collects a sample that has \(2.00 \times 10^{14}\) molecules of carbon dioxide gas. How many grams is this, given that the molar mass of \(\mathrm{CO}_{2}\) is 44.01 \(\mathrm{g} / \mathrm{mol}\) ?

Short Answer

Expert verified

The sample of carbon dioxide gas weighs \(1.46 \times 10^{-8}\) grams.

Step by step solution

Understanding Avogadro's Number

Avogadro's number, which is \(6.022 \times 10^{23} \mathrm{mol}^{-1}\), tells us the number of entities (like atoms or molecules) in one mole of a substance. Therefore, it can be used to convert between the number of molecules and moles.

Convert Molecules to Moles

Divide the given number of molecules, \(2.00 \times 10^{14}\), by Avogadro's number to convert to moles. This gives: \(\frac{2.00 \times 10^{14}}{6.022 \times 10^{23} \mathrm{mol}^{-1}} = 3.32 \times 10^{-10} \mathrm{mol}\).

Convert Moles to Grams

Multiply the number of moles by the molar mass to convert to grams. Given that the molar mass of \(\mathrm{CO}_{2}\) is 44.01 \(\mathrm{g/mol}\), this gives: \(3.32 \times 10^{-10} \mathrm{mol} \times 44.01 \mathrm{g/mol} = 1.46 \times 10^{-8} \mathrm{g}\).

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A scientist collects a sample that has \(2.00 \times 10^{14}\) molecules of carbon dioxide gas. How many grams is this, given that the molar mass of \(\mathrm{CO}_{2}\) is 44.01 \(\mathrm{g} / \mathrm{mol}\) ?

Short Answer

Step by step solution

Understanding Avogadro's Number

Convert Molecules to Moles

Convert Moles to Grams

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