Ideal Gas Law Problems, 5

Category: Chemical Engineering Math

"Published in Newark, California, USA"

A 10 L vessel containing 8.00 grams of O₂ is connected by means of a valve to a 5 L vessel containing 7.00 grams of N₂. When the valve was opened and the gases are allowed to mix, what will be the total pressure of the gas mixture at 25°C assuming the temperature was kept constant?

Solution:

The first thing that we need to do is to get the number of moles of O₂ and N₂. 

The number of moles of O₂ is

The number of moles of N₂ is 

The absolute temperature of the gas mixture is

 
The universal gas law constant for L, gmole, K, and atm is

 .

The partial pressure of O₂ at the gas mixture is

The partial pressure of N₂ at the gas mixture is
 

 

 

 

Therefore, the total pressure of the gas mixture is
 

 

 

Ideal Gas Law Problems, 4

Category: Chemical Engineering Math

"Published in Vacaville, California, USA"

A quantity of 280.7 grams of a hydrate, Na₂CO₃•xH₂O was heated in an oven to drive off water. If the steam produced in a 5L vessel at 110ºC exerted a pressure of 39.6 atm, what is the formula of the hydrate?

Solution:

The first thing that we have to do is to get the amount of steam or water by Ideal Gas Law as follows

The absolute temperature of a gas is  

The universal gas law constant for L, gmole, K, and atm is .  

Hence, the number of moles of water vapor is

The weight of water vapor is

The weight of Na₂CO₃ in Na₂CO₃•xH₂O is

The number of moles of water in Na₂CO₃•xH₂O is

The number of water molecules in Na₂CO₃•xH₂O is

Therefore, the molecular formula of the hydrate is Na₂CO₃•4H₂O.

Dalton's Law of Partial Pressure, 2

Category: Chemical Engineering Math

"Published in Vacaville, California, USA"

Ammonia decomposes completely to hydrogen and nitrogen gas. If the total pressure of the reaction vessel at the end of the reaction is 250 mm Hg, what is the partial pressure of nitrogen gas?

Solution:

Consider the decomposition reaction of ammonia into hydrogen and nitrogen gas as follows

Basis: 2 moles NH₃ = 3 moles H₂ = 1 mole N₂

If the total pressure of the reaction vessel at the end of the reaction is 250 mm Hg, therefore, by Dalton's Law of Partial Pressure, the partial pressure of nitrogen gas is

Ideal Gas Law Problems, 3

Category: Chemical Engineering Math

"Published in Newark, California, USA"

A certain gas weighs 2.478 grams and occupies a volume of 712.5 mL at 25°C and 1.2 atm. What is the molecular formula of the gas?

Solution:

In the given word problem, the weight of a gas is given. We need to solve for the number of moles of a gas in order to get its molecular weight as well as its molecular formula. 

The absolute temperature of a gas is 

The universal gas law constant for L, gmole, K, and atm is 

.

  
Hence, by Ideal Gas Law, the number of moles of a gas is

  

The molecular weight of a gas is
 

 

 

Next, we need to get the Periodic Table of Elements and check the atomic mass of the gas elements (except the noble gasses). The molecular weight of a gas is equal to twice the atomic mass of a gas element. The molecular weight of the gasses are:
 

 

 

 

 

 

By comparing the calculated molecular weight of a gas with the molecular weight of the gasses above, chlorine gas is the closest value.

Therefore, the molecular formula of a certain gas is Cl₂.