Calculate amount of formic acid (ka=2*10-4) which shoud be dissolved in 10L of water to obtain a solution of pH=3.7?

1 Answer
Jun 20, 2018

Answer:

You should use 0.18 g of formic acid.

Explanation:

Step 1. Calculate the desired #["H"_3"O"^"+"]#

#["H"_3"O"^"+"] = 10^"-pH"color(white)(l)"mol/L" = 10^"-3.7"color(white)(l)"mol/L" = 2.0 × 10^"-4"color(white)(l)"mol/L"#

Step 2. Calculate the concentration of formic acid

We can use an ICE table to help with the calculation.

#color(white)(mmmmmml)"HA" + "H"_2"O" ⇌ "H"_3"O"^"+" + "A"^"-"#
#"I/mol·L"^"-1": color(white)(mm)c color(white)(mmmmmmml)0color(white)(mmm)0#
#"C/mol·L"^"-1": color(white)(ml)"-"xcolor(white)(mmmmmml)"+"xcolor(white)(mml)"+"x#
#"E/mol·L"^"-1": color(white)(m)c"-"xcolor(white)(mmmmmmm)xcolor(white)(mmm)x#

#K_text(a) = (["H"_3"O"^"+"]["A"^"-"])/(["HA"]) = x^2/(c-x) = 2.0 × 10^"-4"#

#x^2 = (c-x)(2.0 × 10^"-4") = 2.0 × 10^"-4"c - 2.0 × 10^"-4"x#

#(2.0 × 10^"-4")c = x^2 + 2.0 × 10^"-4"x#

#c = (x^2 + 2.0 × 10^"-4"x)/(2.0 ×10^"-4")#

#x = 2.0 × 10^"-4"#

#c = ((2.0 × 10^"-4")^color(red)(cancel(color(black)(2))) + (2.0 × 10^"-4")^color(red)(cancel(color(black)(2))))/(color(red)(cancel(color(black)(2.0 × 10^"-4")))) = 4.0 × 10^"-4"#

#c = 4.0 × 10^"-4"color(white)(l)"mol/L"#

Step 3. Calculate the moles of formic acid

#"Moles" = 10 color(red)(cancel(color(black)("L"))) × (4.0 × 10^"-4"color(white)(l)"mol")/(1 color(red)(cancel(color(black)("L")))) = 4.0 × 10^"-3"color(white)(l)"mol"#

Step 4. Calculate the mass of formic acid

#"Mass" = 4.0 × 10^"-3" color(red)(cancel(color(black)("mol"))) × "46.03 g"/(1 color(red)(cancel(color(black)("mol")))) = "0.18 g"#