Question

Combustion of hydrocarbons such as hexane (C6H14) produces carbon dioxide, a "greenhouse gas." Greenhouse gases in the Earth's atmosphere can trap the Sun's heat, raising the average temperature of the Earth. For this reason there has been a great deal of international discussion about whether to regulate the production of carbon dioxide.

1. Write a balanced chemical equation, including physical state symbols, for the combustion of liquid hexane into gaseous carbon dioxide and gaseous water. x1 2. Suppose 0.290 kg of hexane are burned in air at a pressure of exactly 1 atm and a temperature of 13.0 °C. Calculate the volume of carbon dioxide gas that is produced Round your answer to 3 significant digits OL

Answer 1

Answer: The volume of carbon dioxide gas is
`4.73* 10^2L`

Step-by-step explanation:

To calculate the number of moles, we use the equation:

`\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}}`

Given mass of hexane = 0.290 kg = 290 g (Conversion factor: 1 kg = 1000 g)

Molar mass of hexane = 86.2 g/mol

Putting values in above equation, we get:

`\text{Moles of hexane}=(290g)/(86.2g/mol)=3.36mol`

The chemical equation for the combustion of hexane follows:

`2C_6H_(14)+19O_2\rightarrow 12CO_2+14H_2O`

By Stoichiometry of the reaction:

2 moles of hexane produces 12 moles of carbon dioxide

So, 3.36 moles of hexane will produce =
`(12)/(2)* 3.36=20.16mol` of carbon dioxide

To calculate the volume, we use the equation given by ideal gas equation:

PV=nRT

where,

P = pressure of the gas = 1 atm

V = Volume of carbon dioxide gas = ?

n = number of moles of gas = 20.16 moles

R = Gas constant =
`0.0821\text{ L  atm }mol^(-1)K^(-1)`

T = temperature of the gas =
`13^oC=[13+273]K=286K`

Putting values in above equation, we get:

`1atm* V=20.16mol* 0.0821\text{ L atm }mol^(-1)K^(-1)* 286K\\\\V=(20.16* 0.0821* 286)/(1)=473.4L`

Hence, the volume of carbon dioxide gas is
`4.73* 10^2L`