Lactic acid builds up in muscle during exercise, and contributes to the feeling of sore muscles afterwards. In blood, a normal amount of lactic acid is between 4.3 and 20.6 mg per dL of blood. What is the smaller number in the range in pounds per gallon? What is the larger number in the range in pounds per gallon?

The smaller number in pounds per gallon is 3.59 × 10⁻⁴ pounds/gallon

The larger number in pounds per gallon is 1.72 × 10⁻³ pounds/gallon

Explanation:

For the smaller number in the range in pounds per gallon (pounds/gallon),

The smaller number in the range is 4.3 mg per dL

First, we will convert 4.3 mg to pounds

(NOTE: 1 g = 0.00220462 pound)

Then, for 4.3 mg in pounds

4.3 mg = 4.3 × 10⁻³ g = 0.0043 g

Now, If 1 g = 0.00220462 pound

Then, 0.0043 g =

(0.0043 × 0.00220462) pound = 9.48 × 10⁻⁶ pound

Also, we will convert dL to gallon

(NOTE: 1L = 0.264172 gallon)

Then, 1 dL = 0.0264172 gallon

Hence, 4.3 mg per dL is 9.48 × 10⁻⁶ pound / 0.0264172 gallon

= 3.59 × 10⁻⁴ pounds/gallon

Hence, the smaller number in pounds/gallon is 3.59 × 10⁻⁴ pounds/gallon

Now, for the larger number in the range in pounds per gallon (pounds/gallon),

The larger number in the range is 20.6 mg per dL

First, convert 20.6 mg to pounds

20.6 mg = 20.6 × 10⁻³ g = 0.0206 g

If 1 g = 0.00220462 pound

Then, 0.0206 g =

(0.0206 × 0.00220462) pound = 4.54 × 10⁻⁵ pound

Recall that, 1 dL = 0.0264172 gallon

Then, 20.6 mg per dL is 4.54 × 10⁻⁵ pound / 0.0264172 gallon

= 1.72 × 10⁻³ pounds/gallon

Hence, the larger number in pounds per gallon is 1.72 × 10⁻³ pounds/gallon

To solve this we use the equation, 

M1V1 = M2V2

where M1 is the concentration of the stock solution, V1 is the volume of the stock solution, M2 is the concentration of the new solution and V2 is its volume.

3 M x 2 mL = M2 x 250 mL

M2 = 0.024 M