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## Q. 3.6

The compound that gives vinegar its sour taste is acetic acid, which contains the elements carbon, hydrogen, and oxygen.

When 5.00 g of acetic acid are burned in air, 7.33 g of $CO_{2}$ and 3.00 g of water are obtained. What is the simplest formula of acetic acid?

 ANALYSIS elements in acetic acid (C, H, and O) mass of acetic acid (5.00 g) result of combustion analysis (7.33 g $CO_{2}$, 3.00 g $H_{2}O$) Information given: molar masses (MM) of $CO_{2}$ and $H_{2}O$ Information implied: simplest formula of acetic acid Asked for:

STRATEGY

1. Find the mass of C and H by using the conversion factors:

$\frac{12.01 g C}{44.01 g CO_{2}}$            $\frac{2(1.008) g H}{18.02 g H_{2}O}$

2. Find the mass of O by difference:
mass of sample = mass of C + mass of H + mass of O
3. Follow the schematic pathway shown in Figure 3.5. ## Verified Solution

 7.33 g $CO_{2}$ × $\frac{12.01 g C}{44.01 g CO_2}$ = 2.00 g C 3.00 g $H_{2}O$ × $\frac{2(1.008) g H}{18.02 g H_{2}O}$ = 0.336 g H 1.  mass of C mass of H mass of O = mass of sample – (mass of C + mass of H) = 5.00 g – (2.00 g + 0.336 g) = 2.66 g 2. mass of O C: $\frac{2.00 g C}{12.01 g/mol}$ = 0.167; H: $\frac{0.336 g H}{1.008 g/mol}$ = 0.333; O: $\frac{2.66 g O}{16.00 g/mol}$ = 0.166 C: $\frac{0.167 mol}{0.166 mol}$ = 1; H: $\frac{0.333 mol}{0.167 mol}$ = 2; O: $\frac{0.166 mol}{0.166 mol}$ = 1 Using the ratios as subscripts, the simplest formula is $CH_{2}O$. 3. mol of each element ratios simplest formula