Please explain the answers thoroughlyas well as all the necessary steps arriving

Question

Please explain the answers thoroughlyas well as all the necessary steps arriving at the answers. Thanks.
A buffer is prepared by mixing 525 mL of 0.50 M formic acid and 475mL of 0.50 M sodium formate. Given Ka= 1.7 X10-4. Calculate the pH using both the the equationfor the ionization showing all additives to the mixture and usingthe Henderson-Hasselbalch equation. Please explain the answers thoroughlyas well as all the necessary steps arriving at the answers. Thanks.
A buffer is prepared by mixing 525 mL of 0.50 M formic acid and 475mL of 0.50 M sodium formate. Given Ka= 1.7 X10-4. Calculate the pH using both the the equationfor the ionization showing all additives to the mixture and usingthe Henderson-Hasselbalch equation. Please explain the answers thoroughlyas well as all the necessary steps arriving at the answers. Thanks.

Explanation / Answer

According to Henderson-Hasselbalch equation
       pH = pKa + log ([salt ] / [acid])        pH = - log Ka +log ([salt ] / [ acid]) No. of moles of formic acid = Molarity * Volume in L                                           = 0.5 * ( 0.525 + 0.475 )                                           = 0.5 mol No. of moles of sodium formate = 0.5 * (0.475 + 0.525 )                                                   =0.5 mol Plug these values we have    pH = - log Ka + log ( 0.5 / 0.5 )          = -log 1.7 X10-4 + 0          = 4 - log1.7          = 4 -0.2304          =3.7696          ~3.8

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