Question

how many molecules of methane, ch4, are in 125 g ch4? (1 mol ch4 = 16.04 g) (1 mol ch4 = 6.02 x 10^{23} molecules) ? x 10^{?} molecules ch4 enter the coefficient in the green box and the exponent in the yellow box.

Explanation:

Step1: Calculate the number of moles of \(CH_4\)

Use the formula \(n=\frac{m}{M}\), where \(m = 125\space g\) (mass of \(CH_4\)) and \(M=16.04\space g/mol\) (molar mass of \(CH_4\)).
\(n=\frac{125\space g}{16.04\space g/mol}\approx7.79\space mol\)

Step2: Calculate the number of molecules of \(CH_4\)

Use Avogadro's number \(N = n\times N_A\), where \(n = 7.79\space mol\) and \(N_A=6.02\times 10^{23}\space molecules/mol\)
\(N=7.79\times6.02\times 10^{23}\space molecules\)
\(N=(7.79\times6.02)\times 10^{23}\space molecules\)
\(7.79\times6.02 = 46.9958\approx4.7\times 10^1\)
So \(N = 4.7\times 10^{24}\space molecules\)

Answer:

Coefficient (green box): \(4.7\), Exponent (yellow box): \(24\)