Question

exercise 6.39 - enhanced - with feedback
missed this? watch kcv: the mole concept, iwe: the mole concept - converting between grams and number of atoms, read section 6.3. you
part a
how many carbon atoms are in a diamond (pure carbon) with a mass of 46 mg?
express your answer using two significant figures.
n = c atoms
submit request answer
provide feedback

Explanation:

Step1: Convert mass from mg to g

We know that \(1\space g = 1000\space mg\). So, for a mass \(m = 46\space mg\), we convert it to grams:
\(m=46\space mg\times\frac{1\space g}{1000\space mg}=0.046\space g\)

Step2: Calculate the number of moles of carbon

The molar mass of carbon (\(M\)) is \(M = 12.01\space g/mol\). Using the formula \(n=\frac{m}{M}\) (where \(n\) is the number of moles and \(m\) is the mass), we have:
\(n=\frac{0.046\space g}{12.01\space g/mol}\approx 0.00383\space mol\)

Step3: Calculate the number of atoms

Using Avogadro's number \(N_A=6.022\times 10^{23}\space atoms/mol\). The number of atoms \(N\) is given by \(N = n\times N_A\)
\(N=0.00383\space mol\times6.022\times 10^{23}\space atoms/mol\)
\(N = 2.306\times 10^{21}\space atoms\approx2.3\times 10^{21}\space atoms\)

Answer:

\(2.3\times 10^{21}\space C\space atoms\)