Answer:
Vb = 18 L option c)
Explanation:
First, we need to write the titration reaction between the base and the acic, which is the following:
Ba(OH)₂ + H₃PO₄ <-------> Ba₃(PO₄)₂ + H₂O
However this equation is not balanced, we need to balance the equation adding some coefficients to the agents so:
3Ba(OH)₂ + 2H₃PO₄ <-------> Ba₃(PO₄)₂ + 6H₂O
Now that the equation is balanced, as we know this is an acid base titration, we need to calculate the mole ratio between the base and acid so:
moles B / moles A = 3/2
2 moles B = 3 moles A (1)
This is taken from the balanced reaction.
Now, finally we use the relation in titration which is:
moles A = moles B
or simply MaVa = MbVb
If we replace this in the ratio of this reaction we have:
2MbVb = 3MaVa (2)
And from there, we solve for Vb which is the volume of the base:
2 * 2 * Vb = 3 * 4 * 6
4Vb = 72
Vb = 72/4
Vb = 18 L
This is the volume of the base required to titrate this acid