9.79 mL
Both HCl and HBr are neutralized by NaOH on a mole per mole basis. So a constant volume of a sodium hydroxide solution will neutralize the same number of moles of either HCl or HBr. So here are the equations to represent what we know and what we want. X = molarity of the Sodium Hydroxide solution and Y = volume of HBr solution to be neutralized.
13.1 * 0.293 = 7.89 * X
Y * 0.765 = 15.4 * X
Solve the first equation for X.
13.1 * 0.293 = 7.89 * X
3.8383 = 7.89 * X
0.486476553 = X
Now substitute the known value of X into the 2nd equation and solve for Y.
Y * 0.765 = 15.4 * 0.486476553
Y * 0.765 = 7.49173891
Y = 9.793122758
Round to 3 significant figures, getting 9.79 ml
