When a 3.0 litre solution of normality N is mixed with 5.0 liter of 4M HCl, then the resultant solution has the normality 10. Find the value of N.

Explanation

Normality (N) is given by the formula: N = (Number of moles of solute) / (Volume of solution in liters) Let's find the number of moles of solute in both solutions before and after mixing. Initial solution (3.0 liters of normality N): Number of moles of solute in the initial solution = N x 3.0 5.0 liters of 4M HCl solution: Number of moles of solute in the 4M HCl solution = 4 x 5.0 Resultant solution (mixture of both solutions with normality 10): Number of moles of solute in the resultant solution = 10 x (3.0 + 5.0) According to the problem, the resultant solution has the normality of 10, so we equate the moles of solute in the resultant solution with the calculated value: 10 x (3.0 + 5.0) = N x 3.0 + 4 x 5.0 Now, we solve for N: 10 x 8.0 = N x 3.0 + 20 80 = 3N + 20 3N = 60 N = 20