Unit 1: Gases and Kinetics

Molecular Mass

The sum of the masses of all atoms comprising the molecule.

Most often (and in this course always) we will be calculating the molecular weight/molecular mass in?

Atomic mass units

Avagadro’s number

6.02214076 × 10 ²3

Conveniently, molecular weight of a molecule calculated using atomic mass units is equal to?

Number of grams of that molecule in one mole

If your sugar
If a sugar cube contained exactly 𝟔. 𝟎𝟐𝟐𝟏𝟒𝟎𝟕𝟔 × 𝟏𝟎 𝟐𝟑 molecules of sugar, your coffee would contain exactly how many moles of sugar?

One

Molar concentration

mol / L is often written as the capital letter 𝑀.

Do not confuse the concentrations expressed in moles with?

Molar concentrations

Imagine that you have 250𝑚𝐿 of a solution at a concentration of 0.5𝑀. It does not matter what molecules the solution contains. It does not even matter if the solution contains a single kind of molecules, or you have made chicken broth and 0.5𝑀 corresponds to the concentration of sodium chloride (salt) that you have added to the broth. You take 50 𝑚𝐿 of the solution from beaker 1 and transfer them into an empty beaker (beaker 2). Next, you take the remaining 200𝑚𝐿 from beaker 1 and transfer them into beaker 3 that contains 200𝑚𝐿 of pure solvent (e.g. water), or if we want to keep using the chicken broth example, beaker 3 contains 200𝑚𝐿 of the unsalted chicken broth).

What is the molar concentrations of NaCl in beakers 2 and 3?

2: Same

3: You dilute something in water. The dilution factor is 2 – you double the volume without increasing the number of the solute molecules. Of course, the concentration of the solute molecules per unit volume should drop by a factor of 2.

The key point when it comes to molar concentrations is that?

You need to track constantly what happens to the number of moles and to the volume.

You can track them separately, and combine when you need to figure out what the molar concentration is.

Just never forget that the number of moles is just another way of expressing?

The number of molecules

When we describe reactions, we use?

Chemical formulas and chemical equations.

When we quantify reactions, we use?

Concentrations (molar concentrations or number of moles– make sure you understand the diJerence) and talk about limiting reactants and reaction
yields.

When we communicate values, we need to always remember about what two things?

Units that accompany the values, and the precision (significant figures) with which we report the data.

Which of the following samples has the largest total number of atoms?
a. 1.00 mol of 𝑁2𝐻4
b. 5.00 mol of 𝐴𝑟
c. 2.00 mol of 𝐶𝑂2
d. 1.00 mol of SF6

D

Limiting Reagant

The starting substance that is completely used up first in a chemical reaction, which stops the reaction from making any more product.

Boyle’s Law

If we take a gas at a low pressure and measure its pressure times its volume, we’ll find out that this product is a constant at a constant temperature and a constant amount of gas (constant number of moles):
𝑝𝑉 = 𝑐𝑜𝑛𝑠𝑡

If we are to plot the dependence of pressure as a function of volume in Boyle’s Law, we expect the graph to look like a?

Hyperbole (y=const/x)

Since the above graph is obtained at a constant temperature, it is called a?

Isotherm

Molecular view of Boyle’s Law

If a sample of gas is compressed to half its volume, then twice as many molecules collide with the walls. As a result, the pressure exerted on the walls is doubled.

Charles’s Law

𝑉 ∝ 𝑇 (𝑤ℎ𝑒𝑛 𝑝 𝑎𝑛𝑑 𝑛 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)

𝑝 ∝ 𝑇 (𝑤ℎ𝑒𝑛 𝑉 𝑎𝑛𝑑 𝑛 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)

Molecular view of Charles’s Law

Raising the temperature of a gas increases the average speed of its constituent atoms or molecules. As a result, the atoms or molecules collide with the walls more frequently and with greater impact. Therefore, they exert a greater pressure.

Avagadro’s Principle

The volume is proportional to the number of moles at a constant pressure and temperature 𝑉 ∝ 𝑛 (𝑤ℎ𝑒𝑛 𝑝 𝑎𝑛𝑑 𝑇 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡)

What happens if you combine Boyle’s, Charles’s, and Avagadro’s laws/principles?

𝒑𝑽 = 𝒏𝑹𝑻
The equation of state for the ideal gas or the ideal gas law

Explain how pv = nRT satisifies each law.

Indeed, when the temperature and the number of moles are constant, then 𝑛𝑅𝑇 is constant – Boyle’s law is satisfied. When 𝑝 and 𝑛 are constant, then 𝑉 is proportional to 𝑇; when 𝑉 and 𝑛 are constant, then 𝑝 is proportional to 𝑇 – Charles’s law is satisfied. Finally, when 𝑝 and 𝑇 are constant, then 𝑉 is proportional to 𝑛 and Avogadro’s principle is satisfied.

The proportionality constant 𝑅 was determined experimentally and has a value of?

𝑅 = 8.31447 𝑃𝑎 𝑚³ 𝑚𝑜𝑙^-1 𝐾^-1

The first kind of problems that you may encounter when dealing with the ideal gas law is the following. You are given three out of four parameters that you can plug into the equation, and you are asked to find a fourth. When dealing with this kind of problems, you always need to remember about?

The units

Sometimes the problem may be complicated. For examples, instead of the number of moles, you may be asked to find mass or density. In this case, you need to?

Combine formulas

The second kind of problems is when you do not have enough information to use the ideal gas law equation, i.e. more than one unknown is present. In this case you may be able to?

Write two or more ideal gas equations and eliminate some of the unknowns by, for example, dividing one equation by the other.

Dalton’s Law

The total pressure of a mixture of non-reacting gases is the sum of the individual partial pressures of each gas

Mole fraction

The number of moles of a component divided by the total number of moles of all components.

Thus, the partial pressure of a gas in a mixture may be calculated by?

Multiplying the mole fraction of the gas by the total pressure.