Question

Suppose that x mL of 40% acid are added to 100mL of 50% acid.

a) Express the concentration C9
b) of the new mixture as a function of x.
c) How much 40% acid should be added to 100 mL of 50% acid to obtain a mixture that is 48% acid?

Answer 1

The concentration C of the acid mixture can be expressed as [(0.4 * x) + 50] / [x + 100], where x is the volume of 40% acid added. To obtain a mixture that is 48% acid by adding 40% acid to 100 mL of 50% acid, approximately 100 mL of 40% acid needs to be added.

Step-by-step explanation:

The student's question pertains to the calculation of a new acid concentration when mixing solutions of different concentrations. To express the concentration C of the mixture as a function of x, we can use the formula:

Concentration of acid in mixture (C) = (amount of acid in portion x + amount of acid in 100 mL) / (total volume of mixture)

For the portion x mL of 40% acid: amount of acid in x mL = (40/100) * x.

For the 100 mL of 50% acid: amount of acid in 100 mL = (50/100) * 100.

Putting it all together, the concentration C is:

C = [(0.4 * x) + 50] / [x + 100].

To find how much 40% acid should be added to 100 mL of 50% acid to get a 48% acid mixture, we solve for x when C is set to 48%:

48 = [(0.4 * x) + 50] / [x + 100],

which simplifies to:

48(x + 100) = (0.4 x) + 50,
48x + 4800 = 0.4x + 50,
47.6x = 4750,
x = 4750 / 47.6,

x = 99.79 mL (approximately 100 mL).