Listen If the percent yield for \( \mathrm{Cr}_{2} \mathrm{~S}_{3} \) ( s ) is \( 52.9 \% \), what theoretical mass (in g ) of \( \mathrm{S}_{8} \) ( s ) is required to produce an experimental 144.7 g of \( \mathrm{Cr}_{2} \mathrm{~S}_{3} \).(s) ? (answer to 1 decimal place) \( \mathrm{MW} \mathrm{S}_{8}=256.8 \mathrm{~g} / \mathrm{mol} \) \[ \begin{array}{c} \mathrm{MW} \mathrm{Cr}_{2} \mathrm{~S}_{3}=200.19 \mathrm{~g} / \mathrm{mol} \\ 16 \mathrm{Cr}(\mathrm{~s})+3 \mathrm{~S}_{8}(\mathrm{~s}) \rightarrow 8 \mathrm{Cr}_{2} \mathrm{~S}_{3}(\mathrm{~s}) \end{array} \] Your Answer: \( \square \) B Answer units
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Mind Expander
To find the theoretical mass of \( \mathrm{S}_{8} \) required to produce 144.7 g of \( \mathrm{Cr}_{2} \mathrm{~S}_{3} \) with a percent yield of 52.9%, we first need to calculate the moles of \( \mathrm{Cr}_{2} \mathrm{~S}_{3} \) produced. Using the molecular weight: \[ \text{Moles of } \mathrm{Cr}_{2} \mathrm{~S}_{3} = \frac{144.7 \text{ g}}{200.19 \text{ g/mol}} = 0.722 \text{ mol} \] Now, since the reaction shows that 8 moles of \( \mathrm{Cr}_{2} \mathrm{~S}_{3} \) are generated from 3 moles of \( \mathrm{S}_{8} \), we can find the moles of \( \mathrm{S}_{8} \) required for this yield: \[ \text{Moles of } \mathrm{S}_{8} = \frac{3}{8} \times 0.722 \text{ mol} = 0.2715 \text{ mol} \] Next, we calculate the theoretical yield of \( \mathrm{Cr}_{2} \mathrm{~S}_{3} \): \[ \text{Theoretical yield} = \frac{144.7 \text{ g}}{0.529} = 273.5 \text{ g} \] Now we find the moles needed for this theoretical yield: \[ \text{Moles of } \mathrm{Cr}_{2} \mathrm{~S}_{3} = \frac{273.5 \text{ g}}{200.19 \text{ g/mol}} = 1.365 \text{ mol} \] And consequently, moles of \( \mathrm{S}_{8} \): \[ \text{Moles of } \mathrm{S}_{8} = \frac{3}{8} \times 1.365 \text{ mol} = 0.511875 \text{ mol} \] The mass of \( \mathrm{S}_{8} \) can now be computed: \[ \text{Mass of } \mathrm{S}_{8} = 0.511875 \text{ mol} \times 256.8 \text{ g/mol} = 131.4 \text{ g} \] So, the theoretical mass of \( \mathrm{S}_{8} \) required is approximately 131.4 g.
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