Category: Chemical Engineering Math
"Published in Newark, California, USA"
Ra-226 decays by alpha emissions. What is its decay product?
Solution:
The given word problem is about nuclear chemistry. Nuclear chemistry is the subfield of chemistry dealing with radioactivity, nuclear processes, such as nuclear transmutation, and nuclear properties. In this type of process, an element can be converted into another kind of element because its atomic number as well as its atomic weight will be changed. There are three types of emissions: alpha emission, beta emission, and gamma emission.
Ra-226 decays by alpha emissions as follows
where X is the unknown element. The atomic number and atomic weight of an unknown element is.
By looking the Periodic Table of Elements, the unknown element is found out to be Radon which is located at Noble Gases.
Hence, the above nuclear equation can be written as follows
Therefore, the decay product Ra-226 is Rn-222. Alpha can also be written as He.
Category: Chemical Engineering Math
"Published in Newark, California, USA"
The osmotic pressure of a dilute aqueous ethyl alcohol solution at 25°C is 38 mm Hg. Calculate the boiling point elevation of this solution.
Solution:
Osmotic pressure is the minimum pressure which needs to be applied to a solution to prevent the inward flow of water across a semipermeable membrane. It is also defined as the measure of the tendency of a solution to take in water by osmosis.
The osmotic pressure of any solution is given by the equation
where
Π = is the osmotic pressure of a solution
M = is the molarity of a solution
R = is the universal gas law constant
T = is the absolute temperature of a solution
The absolute temperature of a solution is
The universal gas law constant for grams, gmole, mm Hg, liters, and K is 
.
Hence, the molarity of ethyl alcohol solution is
The boiling point elevation is defined as the product of the boiling
point constant of a solvent and the molality of a solution.
where m is the molality of a solution.
From the Table of Freezing and Boiling Information of Solvents, the boiling point constant of water is 
.
Since the concentration of ethyl alcohol is in molarity, then we have to convert it into molality as follows
where ρ is the mass density of a solution.
By looking at the Table of Ethyl Alcohol - Water Mixtures, the density in kg/L is almost the same or similar to pure water which has a range from 0.9 to 1.0 kg/L although we increase the concentration of ethyl alcohol from 0 to 50% by weight. In this case, let's approximate that the density of ethyl alcohol solution is 1.00 kg/L.
Hence, the molality of ethyl alcohol solution is
The unit of molality must be gmoles of ethyl alcohol per kg. of water. The weight of ethyl alcohol in 1 liter of solution is
The weight of water in 1 liter of solution is
Since the weight of water is almost equal to the weight of solution, then the molality of ethyl alcohol is equal to
Therefore, the boiling point elevation of ethyl alcohol solution is
Category: Chemical Engineering Math
"Published in Newark, California, USA"
What is the freezing point of a 30% urea, (NH2)2CO solution in water?
Solution:
Basis: 100 grams of 30% (NH2)2CO
The
freezing point constant is defined as the number of degrees the
freezing point will be lowered per mole of solute per 1000 g or 1 kg of
solvent present. This can be written as
where m is the molality of a solution.
The number of moles of (NH2)2CO is
The weight of water is
Hence, the molality of 30% (NH2)2CO solution in water is
From the Table of Freezing and Boiling Information of Solvents, the freezing point constant of water is 
.
The
freezing point depression is defined as the product of the freezing
point constant of a solvent and the molality of a solution.
Hence, the freezing point depression of a solution is
Therefore, the freezing point of 30% (NH2)2CO solution is
Category: Chemical Engineering Math
"Published in Newark, California, USA"
The vapor pressure of water at 25°C is 23.756 torr. A solution consisting of 18.913 grams of a non-volatile substance in 36 grams of water has a vapor pressure of 20.234 torr. What is the molecular weight of the solute?
Solution:
From the description of the given problem above, it is an application of Raoult's Law because it involves the vapor pressures of a solute and a solvent. From this method, we can calculate the amount of a non-volatile solute as well as its molecular weight.
The formula or working equation for Raoult's Law is
where
Psolution = is the vapor pressure of a solution
Xsolvent = is the mole fraction of a solvent
P°solvent = is the vapor pressure of pure solvent
Hence, the mole fraction of a solvent which is water is
Therefore, the molecular weight of a solute is
