Problem 66 - Chemistry The Central Science

Question

In the United States, water used for irrigation is measured in acre-feet. An acre-foot of water covers an acre to a depth of exactly \(1 \mathrm{ft}\). An acre is \(4840 \mathrm{yd}^{2}\). An acre-foot is enough water to supply two typical households for 1.00 yr. (a) If desalinated water costs \(\$ 1950\) per acre-foot, how much does desalinated water cost per liter? (b) How much would it cost one household per day if it were the only source of water?

Step-by-Step Solution

Answer

(a) Desalinated water costs approximately $0.00158 per liter. (b) The daily cost for one household would be about $2.67 if desalinated water were the only source of water.

Step 1: Find the volume of one acre-foot in cubic yards

One acre-foot covers an area of 4840 square yards to a depth of 1 ft. So, the volume of one acre-foot can be calculated as followed: \(volume = area \times depth\) Since 1 acre is equal to \(4840\) square yards and 1 ft is equal to \( \frac{1}{3}\) yards, we have: \(volume = 4840\,\mathrm{yd}^2 \times (\frac{1}{3}\,\mathrm{yd}) = 1613.33\, \mathrm{yd}^3\)

Step 2: Convert cubic yards to liters

We will use the conversion: \(1\, \mathrm{yd}^3 \equiv 764.55\, \mathrm{L}\) So, one acre-foot is equal to: \(1613.33\, \mathrm{yd}^3 \times 764.55\, \mathrm{L/ yd}^3 \approx 1,233,450\, \mathrm{L}\) 2: Calculate cost per liter

Step 3: Calculate the cost per liter

If desalinated water costs $1950 per acre-foot, the cost per liter can be calculated as: \(\mathrm{Cost\, per\, liter} = \frac{\$1950}{1,233,450 \, \mathrm{L}} \approx \$0.00158 \, \mathrm{per\, liter}\) 3: Calculate daily cost for one household

Step 4: Calculate the daily water consumption per household

According to the problem, one acre-foot is enough to supply water to two households for one year (365 days). So, the daily water consumption by one household can be calculated as: \(\mathrm{Water\, consumption\, for\, 1\, household} = \frac{1,233,450\, \mathrm{L}}{2 \times 365 \, \mathrm{days}} \approx 1689.17 \, \mathrm{L/day}\)

Step 5: Calculate daily cost for one household

Now, we can calculate the daily cost for one household using the cost per liter: \(\mathrm{Daily\, cost\, for\, 1\, household} = 1689.17\, \mathrm{L/day} \times \$0.00158\, \mathrm{per\, liter} \approx \$2.67 \, \mathrm{per\, day}\) Answer: (a) Desalinated water costs approximately $0.00158 per liter. (b) The daily cost for one household would be about $2.67 if desalinated water were the only source of water.