Laboratory Mathematics percent solution

Question

 Make 1800 mL of a 50% weight/weight acetone alcohol solution.

1. Specific gravity acetone: 0.786
2. Specific gravity alcohol: 0.810

2. Calculate the dilution using 0.5 mL of urine and 8.5 mL of isotonic saline.

3. Calculate the dilution of 0.1 mL serum in 0.9 mL water.

Answer 1

To make a 50% weight/weight acetone alcohol solution with a total volume of 1800 mL, we need to calculate the amounts of acetone and alcohol required.

Let's denote:

A = volume of acetone (in mL)

B = volume of alcohol (in mL)

The weight of acetone (W_acetone) and the weight of alcohol (W_alcohol) can be calculated using the following formulas:

W_acetone = A * Specific gravity of acetone * Density of water

W_alcohol = B * Specific gravity of alcohol * Density of water

We know that the total weight of the solution should be equal to the sum of the weights of acetone and alcohol:

W_solution = W_acetone + W_alcohol

Since we want a 50% weight/weight solution, the weight of acetone should be half the total weight of the solution:

W_acetone = 0.5 * W_solution

Now, let's substitute the weight formulas and solve for A:

A * Specific gravity of acetone * Density of water = 0.5 * (W_acetone + W_alcohol)

A * 0.786 * 1000 g/L * 1 g/mL = 0.5 * (W_acetone + W_alcohol)

A = 0.5 * (W_acetone + W_alcohol) / (0.786 * 1000)

Similarly, we can find the volume of alcohol, B:

B = 0.5 * (W_acetone + W_alcohol) / (0.810 * 1000)

Now we can substitute the values and calculate A and B:

W_acetone = 0.5 * 1800 mL = 900 g

W_alcohol = 0.5 * 1800 mL = 900 g

A = (0.5 * 1800) / (0.786 * 1000) ≈ 1.146 mL

B = (0.5 * 1800) / (0.810 * 1000) ≈ 1.111 mL

So, to make 1800 mL of a 50% weight/weight acetone alcohol solution, you would mix approximately 1.146 mL of acetone with approximately 1.111 mL of alcohol and then dilute the mixture with enough water to reach a total volume of 1800 mL.

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For the dilution calculations:

Dilution of urine with isotonic saline:

Dilution factor = Volume of final solution / Volume of initial solution

Dilution factor = (0.5 mL + 8.5 mL) / 0.5 mL = 18

Dilution of serum in water:

Dilution factor = Volume of final solution / Volume of initial solution

Dilution factor = (0.1 mL + 0.9 mL) / 0.1 mL = 10