Question

the famous hope diamond at the smithsonian national museum of natural history weighs 45.52 carats. diamond is a crystalline form of carbon. image credit: smithsonian institution, washington d.c./bridgeman images 1st attempt part 1 (1 point) see periodic table how many moles of carbon are in the hope diamond (1 carat = 200 mg)? moles part 2 (1 point) see hint how many carbon atoms are in the diamond?

Explanation:

Step1: Convert carats to grams

Given \(1\) carat \( = 200\space mg=0.2\space g\).
The mass of the Hope Diamond \(m = 45.52\times0.2\space g = 9.104\space g\)

Step2: Calculate moles of carbon

The molar mass of carbon \(M = 12.01\space g/mol\).
Using the formula \(n=\frac{m}{M}\), where \(n\) is the number of moles, \(m\) is the mass, and \(M\) is the molar mass.
\(n=\frac{9.104\space g}{12.01\space g/mol}\approx 0.758\space mol\)

Step3: Calculate number of carbon atoms

Using Avogadro's number \(N_A = 6.022\times 10^{23}\space atoms/mol\)
The number of atoms \(N=n\times N_A\)
\(N = 0.758\times6.022\times 10^{23}\space atoms\approx4.57\times 10^{23}\space atoms\)

Answer:

Part 1: \(0.758\) moles
Part 2: \(4.57\times 10^{23}\) atoms