Answer to Question #257773 in Inorganic Chemistry for shamsa

Question

1. Gases and kinetic molecular theory 1. The behaviour of gases can be described by a number of laws based on experimental observations of their properties. With reference to the ideal gas EQUATION discuss how the molecular theory of gases was developed. 2. Derive an equation that can be used to calculate the density of a gas from its molar mass, pressure, and temperature. 3. What is the density of ethane gas, C2H6, at a pressure of 183.4 kPa and a temperature of 25 °C? 4. What is the pressure in kilopascals in a 35.0 L balloon at 25 °C filled with pure hydrogen gas produced by the reaction of 34.11 g of CaH2 with water? 5. Calculate the volume, in litres, occupied by 1.0 mol of an ideal gas at STP.

Answer 1

1. kinetic theory of gases, assumes that the molecules are very small relative to the distance between molecules. The molecules are in constant, random motion and frequently collide with each other and with the walls of any container.

The individual molecules possess the standard physical properties of mass, momentum, and energy. The density of a gas is simply the sum of the mass of the molecules divided by the volume which the gas occupies. The pressure of a gas is a measure of the linear momentum of the molecules. As the gas molecules collide with the walls of a container, the molecules impart momentum to the walls, producing a force that can be measured. The force divided by the area is defined to be the pressure. The temperature of a gas is a measure of the mean kinetic energy of the gas. The molecules are in constant random motion, and there is an energy (mass x square of the velocity) associated with that motion. The higher the temperature, the greater the motion.

In a solid, the location of the molecules relative to each other remains almost constant. But in a gas, the molecules can move around and interact with each other and with their surroundings in different ways. As mentioned above, there is always a random component of molecular motion. The entire fluid can be made to move as well in an ordered motion (flow). The ordered motion is superimposed, or added to, the normal random motion of the molecules. At the molecular level, there is no distinction between the random component and the ordered component. We measure the pressure produced by the random component as the static pressure. The pressure produced by the ordered motion is called dynamic pressure. And Bernoulli's equation tells us that the sum of the static and dynamic pressure is the total pressure which we can also measure

2.

The relationships between molar mass and density for a monoatomic gas can be easy. The Ideal Gas Law, PV = nRT can be arranged so that n moles equals the mass/molar mass of the gas to become,PV = M
mRT​where m is the mass and M is the molar mass.M = PV
mRT​, if you hold the temperature of the gas constant the equation reduces to the Boyle's law or PV
m​ The mass will be constant assuming the container is closed and so the gas cannot be escaped so, PV will be constant. D = V
m​ and M = PV
mRT​M = P
DRT​The higher the density of the gas the higher the molar mass and vice versa. 

3.We will count out density from the ideal gas law:

PV = m/Mr * RT, were R - ideal gas constant, T - temperature in kelvins; P - pressure, V - volume, m - mass of gas, Mr - molar mass;

T = t + 273.15 = 25 + 273.15 = 298.15 K;

Mr = 12 * 2 + 6 *1 = 30;

P = 183.4 kPa = 183400 Pa;

R = 8.314 m³⋅Pa⋅K⁻¹⋅mol⁻¹;

183400V = m/30 * 8.314 * 298.15;

183400V = 82.63m;

V = 82.63m/183400 = 0.00045m;

Then, the formula of density is:

ρ = m/V = m/0.00045m = 1/0.00045 = 2222.22 g/m³ = 2.22 kg/m³

^4.Solution: CaH2 + 2H2O = Ca(OH)2 + H2

From one mol of CaH2 you get 1 mol H2. The amount of CaH2 is 34.11/42.08=0.81 mol, and it equals to the amount of hydrogen. 25 °C is 25+273.15=298.15 °K. The preasure in the baloone can be calculated by the ideal gas law: P=nRT/V, so P=0.81*8.314*298.15/35.0=57.37 kPa.

Answer: 57.37 kPa.

5 .Ideal gas law

pV=nRT

R = 0.08206 L×atm/mol×K

At STP

p = 1 atm

T= 273 K

$V = \frac{nRT}{p} \\ V= \frac{1.0 \times 0.08206 \times 273}{1} = 22.4 \;L$

Answer: 22.4 L