Abuffer is prepared by adding 100 ml of 0.50 m sodium hydroxide to 100 ml of 0.75 m propanoic acid. is this a buffer solution, and if so, what is its ph?

The is yes, It is a buffer solution.

first, we need to get moles of sodium hydroxide and propanoic acid:

moles NaOH = molarity * volume 
                       
                       = 0.5M * 0.1 L = 0.05 moles

moles propanoic acid = molarity * volume

                                     = 0.75 M * 0.1 L = 0.075 moles

[NaOH] at equilibrium = 0.05 m

[propanoic acid ] at equilibrium = 0.075 - 0.05 = 0.025 m

when Pka for propanoic acid (given) = 4.89 

so by substitution:

∴PH = Pka + ㏒[NaOH]/[propanoic acid ]

∴ PH = 4.89 + ㏒ 0.05 / 0.025

         = 5.19

You would do 1500/4 and the answer is 375