Assume 100 grams of mixture. This means the mass of each compound, in grams, is the same as its percentage. Find the mass of C from CO and from \text{CO}_2 and add these masses together.
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100\text{ g of mixture}=35\text{ g CO and 65 g CO}_2. \\ \text{C from CO}=(35.0\text{ g CO})\left\lgroup\frac{1\text{ mol CO}}{28.01\text{ g CO}} \right\rgroup \left\lgroup\frac{1\text{ mol C}}{1\text{ mol CO}} \right\rgroup \left\lgroup\frac{12.01\text{ g C}}{1\text{ mol C}} \right\rgroup =15.007\text{ g C (unrounded)} \\ \text{C from CO}_2=(65.0\text{ g CO}_2)\left\lgroup\frac{1\text{ mol CO}_2}{44.01\text{ g CO}_2} \right\rgroup \left\lgroup\frac{1\text{ mol C}}{1\text{ mol CO}_2} \right\rgroup \left\lgroup\frac{12.01\text{ g C}}{1\text{ mol C}} \right\rgroup =17.738\text{ g C (unrounded)} \\ \text{Mass percent C}=\left\lgroup\frac{(15.007+17.738)\text{g}}{100\text{ g Sample}} \right\rgroup \times 100\%=32.745=32.7\%\text{ C}