To calculate the percent by mass of each component in the solution, we'll first find the total mass of the mixture and then determine the mass percent of each component.
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Calculate the total mass of the mixture: \[ \text{Total mass} = \text{mass of carbon tetrachloride} + \text{mass of 2-ethyltoluene} + \text{mass of isopropenylbenzene} \] \[ \text{Total mass} = 53.8 , \text{g} + 50.0 , \text{g} + 72.8 , \text{g} = 176.6 , \text{g} \]
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Calculate percent by mass for each component:
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Carbon tetrachloride: \[ \text{Percent by mass} = \left( \frac{\text{mass of carbon tetrachloride}}{\text{total mass}} \right) \times 100 \] \[ \text{Percent by mass (CCl}_4\text{)} = \left( \frac{53.8 , \text{g}}{176.6 , \text{g}} \right) \times 100 \approx 30.5% \]
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2-Ethyltoluene: \[ \text{Percent by mass} = \left( \frac{\text{mass of 2-ethyltoluene}}{\text{total mass}} \right) \times 100 \] \[ \text{Percent by mass (C}9\text{H}{12}\text{)} = \left( \frac{50.0 , \text{g}}{176.6 , \text{g}} \right) \times 100 \approx 28.3% \]
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Isopropenylbenzene: \[ \text{Percent by mass} = \left( \frac{\text{mass of isopropenylbenzene}}{\text{total mass}} \right) \times 100 \] \[ \text{Percent by mass (C}9\text{H}{10}\text{)} = \left( \frac{72.8 , \text{g}}{176.6 , \text{g}} \right) \times 100 \approx 41.2% \]
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Summary of Percent by Mass:
- Carbon tetrachloride: 30.5%
- 2-Ethyltoluene: 28.3%
- Isopropenylbenzene: 41.2%
All values are rounded to three significant digits as requested.
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