Question

Calcium chloride is applied to highways in winter to melt accumulated ice. A snow-plow truck applies 400 lb of CaCl2 per mile of highway. How many formula units of the compound are applied per mile? Note 1 lb = 453.6 g.a) 6 x 10^23 CaCl2 formula units

b) 9 x 10^26 CaCl2 formula units
c) 4 x 10^27 CaCl2 formula units
d) 1 x 10^27 CaCl2 formula units

Answer 1

To calculate the formula units of CaCl2 applied per mile, the pounds must be converted to grams, grams to moles using the molar mass of CaCl2, and then moles to formula units via Avogadro's number, resulting in approximately 9 x 10^26 CaCl2 formula units per mile. So the correct option is b.

Step-by-step explanation:

The student is asking how many formula units of calcium chloride (CaCl2) are applied per mile if a snow-plow truck applies 400 lb of the compound. To find out, we'll first convert pounds to grams then use the molar mass of CaCl2 to find moles, and finally, we'll convert moles to formula units using Avogadro's number.

• Convert pounds to grams: 400 lb * 453.6 g/lb = 181440 g
• Calculate moles from grams: The molar mass of CaCl2 is approximately 110.98 g/mol, so 181440 g / 110.98 g/mol ≈ 1635.43 mol
• Convert moles to formula units: 1635.43 mol * 6.022 x 1023 formula units/mol ≈ 9.85 x 1026 CaCl2 formula units

Therefore, the correct answer is approximately 9 x 1026 CaCl2 formula units per mile, which corresponds to option (b).