Question

Question:Arrange the following substances in order of increasing mass percent of carbon.
a. caffeine, C₈H₁₀N₄O₂
b. sucrose, C₁₂H₂₂0₁₁
c. ethanol, C₂H₅OH

Short answer

Answer

The order of increasing mass percentage of carbon is

$C_{12}{H}_{22}{O}_{11}<C_8{H}_{10}{N}_4{O}_2<C_2{H}_{5}OH$

Step-by-step solution

Finding mass percentage of carbon with caffeine

The mass of 1 mole of caffeine can be denoted as,

$$\begin{gathered} =8(12.010)+10(1.0079)+4(14.006)+2(15.999) \\ =96.08+10.079+56.024+31.998 \\ =194.181 g \end{gathered}$$

Mass percentage can be denoted as,

$$\begin{gathered} \backslash \mathrm{begingathered}\text{Mass} \text{\%} \text{of} \text{carbon}= \left(\frac{\text{Mass} \text{of} \text{carbon}}{\text{Mass} \text{of} \text{1} \text{mole} \text{caffeine}}\right)\times 100 \\ =\frac{96.08}{194.181}\times 100 \\ \text{Mass} \text{\%} \text{of} \text{carbon}=49.47 \%\mathrm{d} \end{gathered}$$

Finding mass percentage of carbon with sucrose

The mass of 1 mole of sucrose can be denoted as,

$$\begin{gathered} =12(12.010)+22(1.0079)+11(15.999) \\ =144.12+22.1738+175.989 \\ =342.28 g \end{gathered}$$

Mass percentage can be denoted as,

$$\begin{gathered} \backslash \mathrm{begingathered}\text{Mass} \text{\%} \text{of} \text{carbon}= \left(\frac{\text{Mass} \text{of} \text{carbon}}{\text{Mass} \text{of} \text{1} \text{mole} \text{sucrose}}\right)\times 100 \\ =\frac{144.12}{342.28}\times 100 \\ \text{Mass} \text{\%} \text{of} \text{carbon}=42.10\% \end{gathered}$$

 Step 3: Finding mass percentage of carbon with ethanol

The mass of 1 mole of ethanol can be denoted as,

$$\begin{gathered} \backslash \mathrm{begingathered}=2(12.010)+5(1.0079)+(15.999)+(1.0079) \\ =24.02+5.0395+15.999+1.0079 \\ =46.0664 g \end{gathered}$$

Mass percentage can be denoted as,

$$\begin{gathered} \backslash \mathrm{begingathered}\text{Mass} \text{\%} \text{of} \text{carbon}= \left(\frac{\text{Mass} \text{of} \text{carbon}}{\text{Mass} \text{of} \text{1} \text{mole} \text{caffeine}}\right)\times 100 \\ =\frac{24.02}{46.0664}\times 100 \\ \text{Mass} \text{\%} \text{of} \text{carbon}=52.14 \%\backslash \end{gathered}$$