Question

1. the combustion of the organic fuel, decane, is outlined in the chemical equation below. you must balance the equation (coefficients are bigger than you may be used to) in order to answer the subsequent questions a - c.

____c₁₀h₂₂ + _o₂ → ____co₂ + ____h₂o
a. how many moles of co₂ are produced if 5.0 moles of c₁₀h₂₂ react with an excess of o₂?
b. how many moles of o₂ react with 0.75 moles of c₁₀h₂₂?
c. how many moles of o₂ would be required to produce 4.0 moles of h₂o?

Explanation:

Step1: Balance the chemical equation

For the combustion of \(C_{10}H_{22}\), we use the method of balancing atoms.

• Carbon atoms: There are 10 carbon atoms in \(C_{10}H_{22}\). So, the coefficient of \(CO_{2}\) is 10.
• Hydrogen atoms: There are 22 hydrogen atoms in \(C_{10}H_{22}\). So, the coefficient of \(H_{2}O\) is 11.
• Oxygen atoms: On the right - hand side, we have \(10\times2 + 11\times1=31\) oxygen atoms. So, the coefficient of \(O_{2}\) is \(\frac{31}{2}\). To get rid of the fraction, we multiply all coefficients by 2.

The balanced equation is \(2C_{10}H_{22}+31O_{2}\to20CO_{2}+22H_{2}O\)

Step2: Solve part (a)

From the balanced equation \(2C_{10}H_{22}+31O_{2}\to20CO_{2}+22H_{2}O\), the mole ratio of \(C_{10}H_{22}\) to \(CO_{2}\) is \(2:20 = 1:10\)
If \(n(C_{10}H_{22})=5.0\space mol\), using the mole ratio \(\frac{n(CO_{2})}{n(C_{10}H_{22})}=\frac{10}{1}\)
\(n(CO_{2})=5.0\space mol\times10 = 50\space mol\)

Step3: Solve part (b)

From the balanced equation, the mole ratio of \(C_{10}H_{22}\) to \(O_{2}\) is \(2:31\)
If \(n(C_{10}H_{22}) = 0.75\space mol\), using the mole ratio \(\frac{n(O_{2})}{n(C_{10}H_{22})}=\frac{31}{2}\)
\(n(O_{2})=0.75\space mol\times\frac{31}{2}=11.625\space mol\)

Step4: Solve part (c)

From the balanced equation, the mole ratio of \(H_{2}O\) to \(O_{2}\) is \(22:31\)
If \(n(H_{2}O) = 4.0\space mol\), using the mole ratio \(\frac{n(O_{2})}{n(H_{2}O)}=\frac{31}{22}\)
\(n(O_{2})=4.0\space mol\times\frac{31}{22}\approx5.64\space mol\)

Answer:

a. \(50\space mol\)
b. \(11.625\space mol\)
c. \(\approx5.64\space mol\)