Question

Gelatin solutions P and Q of concentrations 3.5% and 0.5%, respectively, need to be mixed to obtain a 3% solution R. How much volume (in ml) of P needs to be mixed with 100 ml of Q to obtain R? (Choose the correct option)

• A. 100
• B. 250
• C. 500
• D. 1000

Hint:

When mixing solutions of different concentrations, use the concept of mass balance for the solute (gelatin in this case). The total amount of solute in the final solution should equal the sum of the solutes from the individual solutions.

Answer 1

The Correct Option is C

Let the volume of solution P to be mixed be \( x \) ml.
Step 1: Amount of gelatin in solution P
The concentration of solution P is 3.5%. This means in every 100 ml of solution P, there are 3.5 grams of gelatin.
So, in \( x \) ml of solution P, the amount of gelatin is:
\[ \text{Amount of gelatin in P} = 0.035x \, \text{grams}. \] Step 2: Amount of gelatin in solution Q
The concentration of solution Q is 0.5%. This means in every 100 ml of solution Q, there are 0.5 grams of gelatin.
So, in 100 ml of solution Q, the amount of gelatin is:
\[ \text{Amount of gelatin in Q} = 0.5 \, \text{grams}. \] Step 3: Total amount of gelatin in solution R
We are asked to mix the solutions to obtain a solution R of 3% concentration.
The total volume of the mixed solution is \( x + 100 \) ml (since we are adding \( x \) ml of P to 100 ml of Q).
The concentration of solution R is 3%, which means that the amount of gelatin in the mixture should be 3% of the total volume.
So, the total amount of gelatin in solution R is:
\[ \text{Amount of gelatin in R} = 0.03 \times (x + 100) \, \text{grams}. \] Step 4: Set up the equation
The total amount of gelatin in solution R is the sum of the gelatin from solutions P and Q. So, we have:
\[ \text{Amount of gelatin in R} = \text{Amount of gelatin in P} + \text{Amount of gelatin in Q} \] \[ 0.03 \times (x + 100) = 0.035x + 0.5 \] Step 5: Solve the equation
Now, let's solve for \( x \):
\[ 0.03(x + 100) = 0.035x + 0.5 \] \[ 0.03x + 3 = 0.035x + 0.5 \] Move all the terms involving \( x \) to one side:
\[ 0.03x - 0.035x = 0.5 - 3 \] \[ -0.005x = -2.5 \] Divide both sides by -0.005:
\[ x = \frac{-2.5}{-0.005} = 500 \] Thus, the volume of solution P that needs to be mixed with 100 ml of Q is 500 ml.