# Material balance with a reaction (chemical engineering)

• MickeyBlue
In summary: Thanks for the help!In summary, when calculating the propane content in a mixture of propane and butane, it is necessary to include the amount of oxygen in excess, which is represented by the variable x.
MickeyBlue

## Homework Statement

Felder & Rousseau 4.73 (p. 184)

A mixture of propane and butane is burned with pure oxygen. The combustion products contain 47.4 mole % H2O. After all of the water is removed from the products, the residual gas contains 69.4 mole% CO2 and the balance is O2. What is the mole percent of propane in the fuel?

## Homework Equations

1. Let propane = P
2. Choose 100 mol of the reactant fuel as a basis

## The Attempt at a Solution

[/B]
Set up 2 balanced equations: 1. C3H8 + 5O2 -> 4H2O + 3CO2
2. C4H8 + 13/2O2 -> 5H2O + 4CO2

I assumed a 100% conversion of the reactant gases. I know O2 is in excess. I drew up a reactant table in terms of mol and set Propane in = P and Butane in= 100-P. I then tried to calculate P by setting the mols of water out divided by the total mols out equal to 0.474.

So, what's the problem?

Hello @MickeyBlue! Welcome to Physics Forums!

MickeyBlue said:

## Homework Statement

Felder & Rousseau 4.73 (p. 184)

A mixture of propane and butane is burned with pure oxygen. The combustion products contain 47.4 mole % H2O. After all of the water is removed from the products, the residual gas contains 69.4 mole% CO2 and the balance is O2. What is the mole percent of propane in the fuel?

## Homework Equations

1. Let propane = P
2. Choose 100 mol of the reactant fuel as a basis

## The Attempt at a Solution

[/B]
Set up 2 balanced equations: 1. C3H8 + 5O2 -> 4H2O + 3CO2
2. C4H8 + 13/2O2 -> 5H2O + 4CO2

I assumed a 100% conversion of the reactant gases. I know O2 is in excess. I drew up a reactant table in terms of mol and set Propane in = P and Butane in= 100-P. I then tried to calculate P by setting the mols of water out divided by the total mols out equal to 0.474.
So far so good, with one exception:

You wrote that the butane was $\mathrm{C_4 H_8}$, but I think you meant $\mathrm{C_4 H_{10}}$. Your equations were balanced correctly though, so I assume that was just a minor mistake typing things into the computer.

As a hint for moving forward, don't forget to include the leftover $\mathrm{O_2}$ in your product. Similar to what you did with $P$, make up a variable name to indicate the amount of $\mathrm{O_2}$ in there. I used the variable $x$, but you can use whatever you want.

So your formula, as you have already stated it, should be of this form:

$$\frac {\mathrm{moles \ of \ H_2O}}{(\mathrm{moles \ of \ H_2O}) + (\mathrm{moles \ of \ CO_2}) + (\mathrm{moles \ of \ O_2})} = 0.474$$

After that, take out the $\mathrm{H_2O}$ and do something quite similar except with $\mathrm{CO_2}$ in the numerator (and the ratio value being different).

If you do things right, you'll have two equations and two unknowns ($P$ and $x$). That's enough to solve for $P$.

Chestermiller said:
So, what's the problem?
My final answer for propane was well above 100 and I couldn't understand why.

MickeyBlue said:
My final answer for propane was well above 100 and I couldn't understand why.
Show your work, and perhaps we may be able to point you in the right direction.

Oh! Thank you, I see where I went wrong now. Because of how I added mols of O2 consumed I took it as the amount in excess instead. You're right; this should be enough to get P.

collinsmark

## What is material balance with a reaction in chemical engineering?

Material balance with a reaction in chemical engineering is a method used to track the flow and quantity of materials involved in a chemical reaction. It involves analyzing the inputs and outputs of the reaction in order to determine the overall mass and composition of the system.

## Why is material balance important in chemical engineering?

Material balance is important in chemical engineering because it helps to ensure the efficiency and effectiveness of a chemical process. It allows engineers to identify any discrepancies or losses in materials and make adjustments to improve the overall performance of the system.

## What factors can affect material balance in a chemical reaction?

There are several factors that can affect material balance in a chemical reaction, including incomplete reactions, side reactions, and impurities in the reactants or products. Changes in pressure, temperature, and reaction conditions can also impact material balance.

## How is material balance calculated in a chemical reaction?

Material balance is calculated by accounting for all the inputs and outputs of the system. This includes the initial amounts of reactants, any added or removed materials during the reaction, and the final products. The difference between the input and output amounts is used to determine the material balance.

## What are some common applications of material balance in chemical engineering?

Material balance is commonly used in chemical engineering for process design, optimization, and troubleshooting. It is also important in environmental engineering for waste management and pollution control, as well as in the pharmaceutical industry for drug synthesis and purification processes.

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