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?

Short answer

There are 0.00830 moles of carbon and 99.7 grams of carbon in this diamond.

Step-by-step solution

Convert atoms of carbon to moles of carbon

To convert the given number of carbon atoms to moles, we will use Avogadro's number. To do this, divide the number of carbon atoms by Avogadro's number: Moles of carbon = $\frac{5.0\times {10}^{21}}{(6.022\times {10}^{23})}$

Calculate the moles of carbon

Now, proceed to calculate the moles of carbon: Moles of carbon = $\frac{5.0\times {10}^{21}}{(6.022\times {10}^{23})}=0.00830mol$

Convert moles of carbon to grams of carbon

Now, we will convert the moles of carbon we calculated in the previous step to grams. To do this, use the molar mass of carbon (12.01 g/mol): Mass of carbon (grams) = Moles of carbon × Molar mass of carbon Mass of carbon (grams) = 0.00830 mol × 12.01 g/mol

Calculate the mass of carbon (grams)

Finally, calculate the mass of carbon (grams): Mass of carbon (grams) = 0.00830 mol × 12.01 g/mol = 99.7 g So, there are 0.00830 moles of carbon and 99.7 grams of carbon in this diamond.