Question

Polychlorinated biphenyls (PCB) are environmental and health hazard. They break down very slowly in the environment. The decomposition of PCBs can be represented by the equation:

2 C12H4Cl6 + 23 O2 + 2 H2O --> 24 CO2 + 12 HCl

a) How many moles of water are needed to react 10.0 mol PCB?

b) How many grams of HCl are produced when 15.2 mol H2O react?


c) How many moles of CO2 are produced when 76.5g HCl are produced?


d) How many grams of PCB are reacted when 100.25g CO2 are produced?


e) How many grams of HCl are produced when 2.5kg of PCB react?

Answer 1

2C₁₂H₄Cl₆ + 23O₂ + 2H₂O = 24CO₂ + 12HCl

a) How many moles of water are needed to react 10.0 mol PCB?
According to equation
n(H2O) = n(PCB) = 10.0 mol
Answer: n(H2O) = 10.0 mol

b) How many grams of HCl are produced when 15.2 mol H₂O react?
According to equation the amount of HCl is
n(HCl) = 6 x n(H₂O) = 6 x 15.2 = 91.2 mol
The weight of HCl is
m(HCl) = n(HCl) x M_W(HCl) = 91.2 x ( 1+ 35.5) = 3328.8 g
Answer: m(HCl) = 3328.8 g

c) How many moles of CO₂ are produced when 76.5g HCl are produced?
n(HCl) = m(HCl) / M_W(HCl) = 76.5 / 36.5 = 2.10 mol
According to equation
n(CO₂) = 2n(HCl) = 2 x 2.10 = 4.20 mol
Answer: n(CO₂) = 4.20 mol

d) How many grams of PCB are reacted when 100.25g CO₂ are produced?
M_W(PCB) = 12 x 12 + 4 x 1 + 6 x 35.5 = 361 g/mol
n(CO₂) = m(CO₂) / M_W(CO₂) = 100.25 / 44 = 2.28 mol
According to equation
n(PCB) = n(CO₂) / 12 = 2.28 /12 = 0.19 mol
m(PCB) = n(PCB) x M_W(PCB) = 0.19 x 361 = 68.59 g
Answer: m(PCB) = 68.59 g

e) How many grams of HCl are produced when 2.5kg of PCB react?
n(PCB) = m(PCB) / M_W(PCB) = 2500 / 361 = 6.93 mol
According to equation
n(HCl) = 6n(PCB) = 6 x 6.93 = 41.58 mol
m(HCl) = n(HCl) x M_W(HCl) = 41.68 x 36.5 = 1517.7 g
Answer: m(HCl) = 1517.7 g