Arithmetic Word Problems

Category: Arithmetic

"Published in Vacaville, California, USA"

You collect balls. Suppose you start out with 16. Mike gives you another 17 balls. How many balls do you have at the end?

Solution:

The given word problem is about the application of four basic operations. At the start, you have 16 balls.

If Mike gives you another ball, you will have 16 + 17 = 33 balls at the end. 

Chemical Equilibrium of Gases, 2

Category: Chemical Engineering Math

"Published in Newark, California, USA"

At 3000K and 1 atm, CO₂ is 40% dissociated to CO and O₂. Calculate its percentage dissociation when the pressure is increased to 2 atm.

Solution:

Consider the chemical reaction above as follows

For gases, the equilibrium constant of the above reaction is

At the start of the reaction, the total pressure of CO₂ which is the total pressure of gas mixture is equal to1 atm. At equilibrium, the partial pressure of gases are as follows:
 

 

Hence, the equilibrium constant for the reaction above is

 

For 1 atm, if x is the partial pressure of CO₂ dissociated, then the partial pressure of gases are as follows:

 

If the pressure is increased to 2 atm, then the partial pressure of gases will be multiplied by 2. Substitute the value of partial pressure of gases at the chemical equilibrium equation above, we have

 

Since the above equation cannot be factored by factoring and even synthetic division, then we have to do the trial and error method until we get zero at the right side of the equation. The best way is to use Excel program in solving for the value of x because we can input the formula and we can assign any values of x in the spreadsheet as follows

Photo by Math Principles in Everyday Life

From the Excel spreadsheet, the value of x which is the partial pressure of CO₂ dissociated is 0.33648572 atm since the right side of the equation is very close to zero.

Therefore, the percent of dissociation of CO₂ is  

Ideal Gas Law Problems, 6

Category: Chemical Engineering Math

"Published in Vacaville, California, USA"

PCl_5(g) dissociates into PCl_3(g) and Cl_2(g) when heated at 250°C and 1 atm. If the density of the gas mixture at equilibrium is 4.4 g/L, what is the fraction of PCl_5(g) dissociated?

Solution:

Consider the chemical reactions above as follows

At equilibrium, there are PCl_5(g), PCl_3(g) and Cl_2(g) gas mixture in 1 liter. If the volume of the reaction at equilibrium is 1 liter, then the number of moles of gas mixture at equilibrium is

At the start of the reaction, the volume is also 1 liter. The number of moles of PCl_5(g) which is also the number of moles of gas mixture at the start of the reaction is

Hence, the amount of PCl_5(g) dissociated or converted into PCl_3(g) and Cl_2(g) is 

Therefore, the fraction of PCl_5(g) dissociated is