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Problem 107

One of the compounds used to increase the octane rating of gasoline is toluene (right). Suppose 20.0 $\mathrm{mL}$ of toluene $(d=$ 0.867 $\mathrm{g} / \mathrm{mL}$ ) is consumed when a sample of gasoline burns in air. (a) How many grams of oxygen are needed for complete combustion of the toluene? (b) How many total moles of gaseous products form? (c) How many molecules of water vapor form?

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The complete combustion of octane, $\mathrm{C}_{8} \mathrm{H}_{18},$ a component of gasoline, proceeds as follows:

$$

2 \mathrm{C}_{8} \mathrm{H}_{18}(I)+25 \mathrm{O}_{2}(g) \longrightarrow 16 \mathrm{CO}_{2}(g)+18 \mathrm{H}_{2} \mathrm{O}(g)

$$

(a) How many moles of $\mathrm{O}_{2}$ are needed to burn 1.50 $\mathrm{mol}$ of $\mathrm{C}_{8} \mathrm{H}_{18}$ ?

(b) How many grams of $\mathrm{O}_{2}$ are needed to burn 10.0 $\mathrm{g}$ of $\mathrm{C}_{8} \mathrm{H}_{18}$ ?

(c) Octane has a density of 0.692 $\mathrm{g} / \mathrm{mL}$ at $20^{\circ} \mathrm{C} .$ How many grams of $\mathrm{O}_{2}$ are required to burn 15.0 $\mathrm{gal}$ of $\mathrm{C}_{8} \mathrm{H}_{18}$ (the capacity of an average fuel tank)?

(d) How many grams of $\mathrm{CO}_{2}$ are produced when 15.0 gal of $\mathrm{C}_{8} \mathrm{H}_{18}$ are combusted?

A 32.65 -g sample of a solid is placed in a flask. Toluene, in which the solid is insoluble, is added to the flask so that the total volume of solid and liquid together is 50.00 $\mathrm{mL} .$ The solid and toluene together weigh 58.58 $\mathrm{g}$ . The density of toluene at the temperature of the experiment is 0.864 $\mathrm{g} / \mathrm{mL}$ . What is the density of the solid?