# Calculate the mass of ethyl acetate formed at 25 C from 1.66 moles of acetic acid and 2.17 moles of ethyl alcohol ? . Kc = 4

Apr 29, 2016

The theoretical yield is 110 g of ethyl acetate.

#### Explanation:

We need the volumes of the reactants, so we can calculate the molarities and do the equilibrium calculation.

Volumes

(a) Acetic acid

V_a = 1.66 color(red)(cancel(color(black)("mol"))) × (60.05 color(red)(cancel(color(black)("g"))))/(1 color(red)(cancel(color(black)("mol")))) × "1 mL"/(1.0497 color(red)(cancel(color(black)("g")))) = "95.0 mL"

(b) Ethanol

V_e = 2.17 color(red)(cancel(color(black)("mol"))) × (46.07 color(red)(cancel(color(black)("g"))))/(1 color(red)(cancel(color(black)("mol")))) × "1 mL"/(0.789 color(red)(cancel(color(black)("g")))) = "126.7 mL"

(c) Total volume

${V}_{\text{tot" = V_a + V_e = "95.0 mL + 126.7 mL" = "221.7mL}}$

Initial concentrations

["Acetic acid"] = "1.66 mol"/"0.2217 L" = "7.49 mol/L"

["Ethanol"] = "2.17 mol"/"0.2217 L" = "9.79 mol/L"

The calculations

$\textcolor{w h i t e}{m m m m m m} \text{acetic acid" + "ethanol" ⇌ "ethyl acetate" + "water}$
$\textcolor{w h i t e}{m m m m m m m m} \text{A"color(white)(mml) +color(white)(ml) "B"color(white)(mll) ⇌color(white)(mml) "C"color(white)(mmm) + color(white)(m)"D}$
$\text{I/mol·L"^"-1} : \textcolor{w h i t e}{m m} 7.49 \textcolor{w h i t e}{m m m m} 9.79 \textcolor{w h i t e}{m m m m m l l} 0 \textcolor{w h i t e}{m m m m m l l} 0$
$\text{C/mol·L"^"-1":color(white)(mml)"-"x color(white)(mmmmm)"-} x \textcolor{w h i t e}{m m m m m} + x \textcolor{w h i t e}{m m m m} + x$
$\text{E/mol·L"^"-1} : \textcolor{w h i t e}{m m} 7.49 - x \textcolor{w h i t e}{m} 9.79 - x \textcolor{w h i t e}{m m m m} x \textcolor{w h i t e}{m m m m m l l} x$

K_"c" = (["C"]["D"])/(["A"]["B"]) = (x·x)/((7.49-x)(9.79-x)) = 4

${x}^{2} = 4 \left(7.49 - x\right) \left(9.79 - x\right) = 4 \left(73.33 - 17.28 x + {x}^{2}\right) = 293.3 - 69.12 x + 4 {x}^{2}$

$3 {x}^{2} - 69.12 x + 293.3 = 0$

$x = 5.61$

The equilibrium concentration of ethyl acetate is 5.61 mol/L.

If the volume change is minimal, the mass of ethyl acetate formed is

0.2217 color(red)(cancel(color(black)("L"))) × (5.61 color(red)(cancel(color(black)("mol"))))/(1 color(red)(cancel(color(black)("L")))) × "88.10 g"/(1 color(red)(cancel(color(black)("mol")))) = "110 g"

The theoretical yield of ethyl acetate is 110 g.