If it requires 23.4 milliliters of 0.65 molar barium hydroxide to neutralize 42.5 milliliters of nitric acid, solve for the molarity of the nitric acid solution. show all of the work used to solve this problem.

unbalanced equation: ba(oh)2 + hno3 yields ba(no3)2 + h2o

Volume Ba(OH)2 = 23.4 mL in liters : 

23.4 / 1000 => 0.0234 L

Molarity  Ba(OH)2 = 0.65 M

Volume HNO3 = 42.5 mL in liters:

42.5 / 1000 => 0.0425 L

number of moles Ba(OH)2 :

n = M x V

n = 0.65 x 0.0234 

n = 0.01521 moles of Ba(OH)2

Mole ratio :

Ba(OH)2 + 2 HNO3 = Ba(NO3)2 + 2 H2O

1 mole Ba(OH)2 2 moles HNO3
 0.01521 moles moles HNO3

moles HNO3 = 0.01521 x 2 / 1

moles HNO3 = 0.03042 / 1

= 0.03042 moles HNO3

Therefore:

M ( HNO3 ) = n / volume ( HNO3 )

M ( HNO3 ) =  0.03042 / 0.0425

M ( HNO3 ) = 0.715 M

The mass has escaped into a gas which you can not see so the law stays true.