Question 4.13: Chemical Formulas as Conversion Factors Hydrogen may replace...
Chemical Formulas as Conversion Factors
Hydrogen may replace gasoline as a fuel in the future. Most major automobile companies are developing vehicles that run on hydrogen. These cars are environmentally friendly because their only emission is water vapor. One way to obtain hydrogen for fuel is to use an emissionfree energy source such as wind power to form elemental hydrogen from water. What mass of hydrogen (in grams) is contained in 1.00 gallon of water? (The density of water is 1.00 g/mL.)
SORT You are given a volume of water and asked to find the mass of hydrogen it contains. You are also given the density of water.
GIVEN: 1.00 gal H_2O
d_{H2O} = 1.00 g/mL
FIND: g H
STRATEGIZE The first part of the conceptual plan shows how to convert the units of volume from gallons to liters and then to milliliters. It also shows how you can then use the density to convert mL to g. The second part of the conceptual plan is the basic sequence of
mass\longrightarrow moles\longrightarrow moles\longrightarrow mass.
Convert between moles and mass using the appropriate molar masses, and convert from mol H_2O to mol H using the conversion factor derived from the molecular formula.
CONCEPTUAL PLAN
RELATIONSHIPS USED
3.785 L = 1 gal
1 \ mL = 10^{-3} L
1.00 g H_2O= 1 mL H_2O (density of H_2O)
molar mass H_2O = 2(1.008) + 16.00 = 18.02 g/mol
2 mol H: 1 mol H_2O
1.008 g H = 1 mol H
SOLVE Follow the conceptual plan to solve the problem.
1.00 \cancel{gal \ H_2O}\times \frac{3.785 \ \cancel{L}}{1 \ \cancel{gal}} \times \frac{1 \ \cancel{mL}}{10^{-3} \ \cancel{L}}\times \frac{1.0 \ g}{\cancel{mL}}=3.7\underline{8} 5 \times 10^3 \ g H_2O
3.7\underline{8} 5 \times 10^3 \ \cancel{g \ H_2O} \times \frac{1 \cancel{mol \ H_2o}}{18.02 \ \cancel{g \ H_2o}}\times \frac{2 \cancel{mol \ H} }{1 \cancel{mol \ H_2o}} \times \frac{1.008 g \ H}{1 \cancel{mol \ H}} =4.23\times 10^{2}g \ H
CHECK The units of the answer (g H) are correct. Since a gal of water is about 3.8 L, its mass is about 3.8 kg. H is a light atom, so its mass should be significantly less than 3.8 kg, as it is in the answer.