Ideal Gas Law Problems

Category: Chemical Engineering Math

"Published in Newark, California, USA"

 What is the volume of 18.0 grams of pure water at 4°C and 1 atm?

Solution:

From the given word problem, it is about Ideal Gas Law because the weight, temperature, and pressure of pure water are given and we need to solve for the volume. 

The Ideal Gas Law is given by the equation

where:  

P = pressure of a gas or vapor
V =  volume of a gas or vapor
n = moles of a gas or vapor
T = absolute temperature of a gas or vapor
n = universal gas law constant

The number of moles of pure water is
 

 

The absolute temperature of pure water is 
 

 

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

Therefore, the volume of pure water is
 

 

 

Separation of Variables - Arbitrary Constant, 14

Category: Differential Equations

"Published in Newark, California, USA"

Find the particular solution for

when x = x₀; v = v₀.

Solution:

Consider the given equation above  

By separation of variables, transfer dx to the right side of the equation as follows 

Integrate on both sides of the equation, we have 

Substitute the values of v and x in order to solve for C as follows 

Therefore, the particular solution is