Answer to Question #235277 in General Chemistry for Chanchan

Question

To make 2.000 gal of a powdered sports drink, a group of students measure out 2.000 gal of water with 500.-mL, 50.-mL, and 5-mL graduated cylinders. Show how they could get closest to 2.000 gal of water, using these cylinders the fewest times.

Answer 1

The relation between volume unit’s gallon and milliliter is given below:

1 gal = 3785.41 mL

The volume of water (V) is 2.000 gal. Convert the volume to milliliters with the above relation.

$2.000 \;gal \times \frac{3785.41 \;mL}{1 \;gal}= 7.571 \times 10^3 \;ml$

≈7570 \;ml

So volume of the water is 7570. mL.

The cylinders available to students for measuring the water are given below:

Cylinder A: 500 ml

Cylinder B: 50 ml

Cylinder C: 5 ml

Split the volume of water (7570. mL) as sum of four digit and two digit numbers as follows:

7570 = (7500 + 50 +20) ml

Now represent the volumes to appropriate number of cylinders A, B and C.

7570 = 15(500 ml) + 1(50 ml) +4(5 ml)

= 15 (Vol of cylinder A) + 1(Vol of cylinder B) + 4(Vol of cylinder C)

Thus, to measure water of volume 7570. mL, number of the cylinders needed are given below:

15(500 ml), 1(50 ml), 4(5 ml)