Question

A website promoting the use of alternative energy vehicles and hybrid technologies claims that "A typical automobile in the USA uses about 40 gal of gasoline every month, producing about 750 lb of carbon dioxide." To determine the truth of this statement, calculate how many pounds of carbon dioxide are produced when 40.00 gal of gasoline are combusted. Assume that the primary ingredient in gasoline is octane, C8H18(l), which has a density of 0.703 g·mL−1.

Answer 1

Answer:

The statement is FALSE

Explanation:

We list the variables we were given:

40 gal = 3.785 * 40 = 151.4 L = 151,400 mL, ρ = 0.703 g/mL

Using the formula, ρ = m ÷ V ⇒ m = ρ · V

m = ρ · V = 0.703 x 151,400 = 106434.2 g = 106.4342 kg

m ≈ 106.4 kg

To convert to lb, multiply the mass value by 2.205

m = 234.6 lb

The combustion reaction is given as:

2$C_{8}H_{18}$ + 25$O_{2}$  ------------>  16$CO_{2}$ + 18$H_{2}O$

C = 14 g, H = 1 g, O = 16 g

$C_{8}H_{18}$ = 14 * 8 + 1 * 18 = 112 + 18 = 130 g, $O_{2}$ = 16 * 2 = 32 g,

$CO_{2}$ = 14 + (16 * 2) = 14 + 32 = 46 g,  $H_{2}O$ = (1 * 2) + 16 = 2 + 16 = 18 g

2$C_{8}H_{18}$ + 25$O_{2}$  ------------>  16$CO_{2}$ + 18$H_{2}O$

(130 * 2) g + (25 * 32) g ----------> (16 * 46) g + (18 * 18) g

260 g + 800 g -------------> 736 g + 324 g

260 g of $C_{8}H_{18}$ produces 736 g of $CO_{2}$

For 40gal (234.6 lb) of $C_{8}H_{18}$ we have:

260 g = 736 g

234.6 lb = x

x = 234.6 * 736 ÷ 260 = 664.1 lb

234.6 lb (40 gal) of  $C_{8}H_{18}$ produces 664.1 lb of $CO_{2}$

234.6 lb (40 gal) of gasoline produces about 664.1 lb of carbon dioxide

This is lesser (by 86.9 lb) than what was stated by the website

Hence, the statement "A typical automobile in the USA uses about 40 gal of gasoline every month, producing about 750 lb of carbon dioxide." is FALSE