Problem 48 - Chemistry An Atoms First Approach

Question

A diamond contains \(5.0 \times 10^{21}\) atoms of carbon. What amount (moles) of carbon and what mass (grams) of carbon are in this diamond?

Step-by-Step Solution

Answer

The diamond contains \( 8.304 \times 10^{-3} \) moles of carbon and \( 9.970 \times 10^{-2} \) grams of carbon.

Step 1: Recall Avogadro's number and the molar mass of carbon

First, we need to recall Avogadro's number, which is the number of particles (such as atoms) per mole of a substance. Avogadro's number is approximately \(6.022 \times 10^{23} \) particles per mole. We also need to know the molar mass of carbon, which is approximately \(12.01\) grams per mole.

Step 2: Convert atoms of carbon to moles of carbon

Given that the diamond contains \(5.0 \times 10^{21}\) atoms of carbon, we can use Avogadro's number to calculate the number of moles of carbon in the diamond: Moles of carbon = \( \frac{atoms \ of \ carbon}{Avogadro's \ number} \) Moles of carbon = \( \frac{5.0 \times 10^{21}}{6.022 \times 10^{23}} \) Moles of carbon = \(8.304 \times 10^{-3} \) moles

Step 3: Convert moles of carbon to grams of carbon

Now we can use the molar mass of carbon to convert the moles of carbon calculated in step 2 to grams of carbon: Mass of carbon = Moles of carbon × Molar mass of carbon Mass of carbon = \( 8.304 \times 10^{-3} \ moles \times 12.01 \ g/mol \) Mass of carbon = \( 9.970 \times 10^{-2} \) grams

Step 4: Write the final answer

Thus, the diamond contains \( 8.304 \times 10^{-3} \) moles of carbon and \( 9.970 \times 10^{-2} \) grams of carbon.