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2. A compound is composed of 39.9987% C, 6.7142% H, and the rest O by mass. When 1.4214 g sample is completely combusted 0.3472 g CO_(2)(g) forms. Find the formula of the compound. A) C_(6)H_(12)O_(6) B) C_(5)H_(12)O_(2) C) C_(6)H_(15)O_(3) D) C_(4)H_(10)O_(2) E) C_(3)H_(6)O_(3)
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To find the formula of the compound, we need to determine the moles of each element present in the compound.<br /><br />Given:<br />- 39.9987% C<br />- 6.7142% H<br />- The rest is O<br /><br />Step 1: Calculate the moles of each element in the compound.<br />- Moles of C = (39.9987 / 12.01) = 3.33<br />- Moles of H = (6.7142 / 1.008) = 6.66<br />- Moles of O = (100 - 39.9987 - 6.7142) / 16.00 = 4.00<br /><br />Step 2: Determine the empirical formula by finding the ratio of the moles of each element.<br />- C: 3.33<br />- H: 6.66<br />- O: 4.00<br /><br />Divide each by the smallest number of moles (4.00):<br />- C: 3.33 / 4.00 = 0.83<br />- H: 6.66 / 4.00 = 1.67<br />- O: 4.00 / 4.00 = 1<br /><br />Step 3: Round the ratios to the nearest whole number.<br />- C: 0.83 ≈ 1<br />- H: 1.67 ≈ 2<br />- O: 1<br /><br />Therefore, the empirical formula of the compound is C1H2O1.<br /><br />Step 4: Verify the empirical formula with the given information about the combustion reaction.<br />- 1.4214 g sample completely combusted to form 0.3472 g CO2.<br />- Moles of CO2 = 0.3472 / 44.01 = 0.0079<br />- Moles of C in CO2 = 0.0079 * 1 = 0.0079<br />- Moles of C in the compound = 0.0079 * 12.01 = 0.0947 g<br />- Moles of H in the compound = 0.0079 * 2 = 0.0158 g<br />- Moles of O in the compound = 1.4214 - 0.0947 - 0.0158 = 1.3109 g<br /><br />Step 5: Calculate the moles of each element in the compound.<br />- Moles of C = 0.0947 / 12.01 = 0.0079<br />- Moles of H = 0.0158 / 1.008 = 0.0157<br />- Moles of O = 1.3109 / 16.00 = 0.0822<br /><br />Step 6: Determine the molecular formula by finding the ratio of the moles of each element.<br />- C: 0.0079<br />- H: 0.0157<br />- O: 0.0822<br /><br />Divide each by the smallest number of moles (0.0079):<br />- C: 0.0079 / 0.0079 = 1<br />- H: 0.0157 / 0.0079 = 2<br />- O: 0.0822 / 0.0079 = 10.41<br /><br />Step 7: Round the ratios to the nearest whole number.<br />- C: 1<br />- H: 2<br />- O: 10<br /><br />Therefore, the molecular formula of the compound is C1H2O10.<br /><br />Answer: E) $C_{3}H_{6}O_{3}$
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