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Answer to Question #57776 in General Chemistry for Tony lundy

Question #57776
A bathroom cleaning is, by weight, 5.8% citric acid (H3C6H5O7, 192.1235g/mol), 8.75% dipropylene glycol butoxy ether (C9H20O3, 190.28288g/mol), 842 PPM limonene (C10H16, 136.2364g/mol) and the rest water.
The density of the butoxy ether is 0.907g/mL and the density of the solution is 1.042g/cm3. Calculator the concentration of citric acid in m and N, the butoxy ether in M and Volume % and the limonene in X and m. Report value a minimum of 4 decimal places.

X (H3C6H5O7)=
Vol% (C9H20O3)=
M (C10H16)=
N (H3C6H5O7)=
m (C9H20O3)=
X (C10H16)=
Expert's answer
Weight of 1 liter of solution is
msol = 1000*1.042 = 1042 g

The weight of the components contained in 1 liter of solution:
m(H3C6H5O7) = 5.8*1042/100 = 60.43600 g
m (C9H20O3) = 8.75*1042/100 = 91.17500 g
m (C6H16) = 842*1042/100000 = 0.87736 g
m (H2O) = 1042 – (60.43600 + 91.17500 + 0.87736) = 889.51164 g

The number of moles of the components in one liter of solution:
n(H3C6H5O7) = 60.43600/192.1235 = 0.31457 mol
n(C9H20O3) = 91.17500/190.28288 = 0.479155 mol
n (C6H16) = 0.87736/136.2364 = 0.006440 mol
n (H2O) = 889.51164/18.01528 = 49.37540 mol
n(Σ) = 0.31457 + 0.479155 + 0.006440 + 49.37540 = 50.17556 mol

Calculate:
X (H3C6H5O7) = n(H3C6H5O7)*100/n(Σ) = 0.31457*100/50.17556 = 0.62694 %
X (C10H16) = n(C10H16)*100/n(Σ) = 0.006440*100/50.17556 = 0.012835%

M (C10H16) = n (C6H16)/Vsol = 0.006440/1 = 0.006440 M

Citric acid is tribasic, so
N (H3C6H5O7) = 3n(H3C6H5O7)/ Vsol = 3*0.31457/1 = 0.94371N

V(C9H20O3) = m(C9H20O3)/ρ(C9H20O3) = 91.17500/0.907 = 100.52370 ml
Vol% (C9H20O3) = V(C9H20O3)*/ Vsol = 100.52370*100/1000 = 10.05237%

Answer:
X (H3C6H5O7) = 0.62694 %
Vol% (C9H20O3) = 10.05237%
M (C10H16) = 0.006440 M
N (H3C6H5O7) = 0.94371N
m (C9H20O3) = 91.17500 g
X (C10H16) = 0.012835%

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