Answer:
The farthest the vehicle could travel (if it gets 20.0 miles per gallon on liquid gasoline) is 1.62 miles.
Explanation:
The automobile gas tank has a volume capacity of 15 gallons which can be converted to liters: 15 × 3.7854 = 56.781 liters
We can find the moles of gasoline by using the ideal gas equation: PV = nRT.
Make n (number of moles) the subject of the formula: n = PV/RT, where:
P = 747 mmHg
V = 56.781 liters
R (universal gas constant) = 0.0821 liter·atm/mol·K
T = 25 ∘C = (273 + 25) K = 298 K
1 atm (in the unit of R) = 760 mmHg
Therefore n = 747 × 56.781/(0.0821 × 760 × 298) = 2.281 mol.
Given that the molar mass of the gasoline = 101 g/mol,
the mass of gasoline = n × molar mass of gasoline = 2.281 mol × 101 g/mol = 230.38 g
the density of the liquid gasoline = 0.75 g/mL
In order to calculate the distance the vehicle can travel, we have to calculate volume of gasoline available = mass of the liquid gasoline ÷ density of liquid gasoline
= 230.38 g ÷ 0.75 g/mL = 307.17 mL = 0.3071 liters = 0.3071 ÷ 3.7854 = 0.0811 gallons
since the vehicle gets 20.0 miles per gallon on liquid gasoline, the distance traveled by the car = gallons available × miles per gallon = 0.0811 × 20 = 1.62 miles.
