Gravimetric Analysis Problems, 2

Category: Chemical Engineering Math

"Published in Newark, California, USA"

A sample containing NaBr and KBr only weighs 253.02 mg. The sample was dissolved in water and treated with excess AgNO₃. The precipitate formed was found to weigh 429.85 mg. Calculate the %NaBr in the sample.

Solution:

If the solution of the mixture of NaBr and KBr is treated with AgNO₃, then AgBr yellow crystal will be formed which is insoluble in water. The chemical reaction for the formation of AgBr is written as follows

If the word statement says "A sample containing NaBr and KBr only weighs 253.02 mg", then the first working equation is

where x is the weight of NaBr and y is the weight of KBr in the mixture.

By gravimetric analysis, we can calculate the amount of AgBr crystals formed from the mixture of NaBr and KBr using their molecular weights as their factor. 

The amount of AgBr formed from NaBr is

The amount of AgBr formed from KBr is

If the word statement says "The precipitate formed was found to weigh 429.85 mg.", then the next working equation is

Let's consider the two working equations as follows

Multiply the first equation by -1.577873 and then add it to the second equation, we have

 -------------------------------------------------------

 

Hence, the weight of NaBr in the mixture is 0.123948 grams.

Therefore, the %NaBr in the mixture is
 

 

 

Molarity of a Solution Problems, 2

Category: Chemical Engineering Math

"Published in Newark, California, USA"

Calculate the molar concentration of a solution that is 30% wt. NH₄NO₃ and has a specific gravity of 1.1252.

Solution:

The concentration of a given solution by percent of weight can be written as follows

Since the specific gravity of a solution which is also the density of a solution is given in the problem, then we can express the concentration of a solution in grams of NH₄NO₃ per liter of solution as follows

The molarity of a solution is defined as moles of solute per liter of solution. Therefore, the molarity of NH₄NO₃ solution is

Normality of a Solution Problems

Category: Chemical Engineering Math

"Published in Newark, California, USA"

What is the normality of a sulfuric acid solution that is 18 M?

Solution:

The molarity of a solution is defined as moles of solute per liter of solution. The given concentration of sulfuric acid solution can be written as follows

Let's consider the ionization of sulfuric acid as follows

Hydrogen ion has an oxidation number of 1 and sulfate ion has an oxidation number of 2. The number of equivalence of a solute is defined as the product of the number of positive ions in a metal ion and the number of negative ions in a non-metal ion. In this case, the number of equivalence of sulfuric acid is 1 x 2 = 2.

The normality of a solution is defined as the number of equivalence of a solute per liter of solution.

Therefore, the normality of a sulfuric acid solution is

Exponential Decay Problems, 3

Category: Chemical Engineering Math, Differential Equations

"Published in Newark, California, USA"

How old is a bottle of wine if the tritium ³H content is 45% of a new wine? The half-life of tritium is 12.5 years.

Solution:

From the description of a given problem, it is about exponential decay problem. The rate of change of a substance is directly proportional to the negative of its substance present. The working equation can be expressed as follows

where

x = amount of tritium at time t
t = decaying time of tritium
k = proportional constant for decaying

By separation of variables, transfer x to the left side of the equation and dt to the right side of the equation as follows

Integrate on both sides of the equation, we have

Take the inverse natural logarithm on both sides of the equation, we have

If x = x₀ and t = 0 at the start, then the value of C is 

Hence, the particular solution of the working equation is

If x = ½ x₀ at t = 12.5 years, then the value of k is 

Take natural logarithm on both sides of the equation, we have 

Hence, the complete working equation of the above equation is 

If x = 0.45 x₀ as stated in the problem, therefore, the age of a bottle of wine that contains tritium is 

Take the natural logarithm on both sides of the equation,w e have