Respuesta :
The correct answer is 2.5 g.
Let x be the mass of NaOH in grams
The molar mass of NaOH = 40.0 gms/mol
Moles of NaOH = mass / molecular mass of NaOH
= x grams / 40.0 gms /mol = 0.025 x mol
Initial moles of CH₃COOH = volume × concentration of CH₃COOH
= 500 / 1000 × 0.20 = 0.1 mol
CH₃COOH + NaOH ⇒ CH₃COONa + H2O
Moles of CH₃COOH left = initial moles of CH₃COOH - moles of NaOH = 0.1 - 0.025x mol
Moles of CH₃COONa formed = moles of NaOH = 0.025x mol
Henderson-Hasselbalch equation:
pH = pKa + log ([CH₃COONa] / [CH₃COOH])
= pKa + log (moles of CH₃COONa /moles of CH₃COOH)
5.0 = 4.76 + log [0.025a / (0.1 - 0.025a)]
log [0.025a / (0.1 - 0.025a)] = 0.24
0.025a / (0.1 - 0.025a) = 10^0.24 = 1.738
0.068445a = 0.17378
a = 0.17378 / 0.068445
= 2.54 g
Mass of NaOH = a = 2.54 g or 2.5 g
The mass of NaOH is 2.54 g.
What is sodium hydroxide?
Sodium hydroxide is an inorganic compound with the chemical formula NaOH. It is also called caustic soda and lye. It is white solid.
Given,
Let the mass be x
Molar mass 40 grams
Calculate the moles of NaOH
mass / molecular mass
[tex]\bold{\dfrac{x}{40\;g/mol} = 0.025x mol}[/tex]
Initial Moles of acetic acid =
[tex]\bold{volume \times concentration\; of\; CH_3COOH}\\\\\bold{\dfrac{500}{1000\times0.20}\times 500 = 0.1 mol}[/tex]
[tex]\bold{CH_3COOH + NaOH= CH_3COONa + H2O}[/tex]
Moles of CH₃COOH left = [tex]Initial\; moles\; of\; CH_3COOH - moles\; of\; NaOH[/tex]
= 0.1 – 0.025x mol
Moles of CH₃COONa formed = moles of NaOH = 0.025x mol
Now, by Henderson-Hasselbalch equation:
[tex]pH = pK_a + log_1_0 ( \dfrac{[A^-]}{[HA]} )[/tex]
[tex]pH = pK_a + log_1_0 ( \dfrac{[CH_3COONa]}{[CH_3COOH]} )[/tex]
[tex]5.0 = 4.76 + log_1_0 ( \dfrac{[0.025a]}{[0.1 - 0.025a]} ) = 0.24[/tex]
[tex]\dfrac{0.025a}{(0.1 - 0.025a)} = 10^0.24 = 1.738[/tex]
0.068445a = 0.17378
[tex]a = \dfrac{0.17378}{0.068445} = 2.54 g[/tex]
Thus, the mass of NaOH is 2.54 gram.
Learn more about sodium hydroxide, here:
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Mass of NaOH = a = 2.54 g or 2.5 g
