Test: Ideal Gas - EmSAT Achieve MCQ

From the ideal gas equation PV = nRT. . . . . . . . .(1)
In the process PV = constant, Temperature T must be constant.

We are also known as, P M = ρ R T

Compare equation (2) with the equation of the straight line, y = mx + C, where m= slope, and c= intercept.
So, m = RT/M = slope which is positive and y-intercept, c = 0, y = P, x = ρ 
Hence, the straight line passes through the origin with a positive slope.

The formula to derive the root mean square speed is given as:

where:

• V_rms is the root mean square speed,
• k is Boltzmann's constant (1.38 x 10^-23 J/K),
• T is the temperature in Kelvin (K),
• m is the molecular mass of the gas in kilograms (kg).
• Here the root mean square speed is dependent on the mass of the molecules: for a given temperature, lighter molecules will move faster than heavier ones.
• However, you asked for the root mean square speeds of molecules of ideal gases at the same temperature. If we consider this condition but we don't specify which gases we are considering, we cannot provide specific numerical values since the rms speed would still vary depending on the molecular mass of each specific gas.
• If you're referring to the comparison between different gases at the same temperature, the lighter gas molecules will have higher root-mean-square speeds than heavier ones, given that they are at the same temperature.
• This means,
• The root mean square speed of molecules of ideal gases at the same temperature is Inversely proportional to the square root of the molecular weight

Boyle's law

• According to Boyle's law, For a given mass of an ideal gas at a constant temperature, the volume of a gas is inversely proportional to its pressure i.e.

• P₁V₁ = P₂V₂
• Therefore, Boyle's law holds for an ideal gas during isothermal changes. 

• The statement that equal volumes of all gases, when measured at the same temperature and pressure, contain an equal number of particles is known as Avogadro's law.
• It was proposed by Amedeo Avogadro, an Italian scientist, in the early 19th century.

Ideal gas law is PV = nRT, which does not involve time.

PV = nRT, => P*5 = 0.0821*300, => P = 5.3 atm.

Density of CO₂ = PM/RT = 1*44/(0.0821*300) = 1.78 g/L, => Specific gravity = 1.78/1 = 1.78.

Charles law:

If the pressure remaining constant, the volume of the given mass of a gas is directly proportional to its absolute temperature.
i.e. V ∝ T
or V/T = constant

• At constant pressure, the volume of the gas is directly proportional to its absolute temperature. This is the statement of Charles law. Thus option 1 is correct.
• For a given mass of an ideal gas at a constant temperature, the volume of a gas is inversely proportional to its pressure. This is the statement of Boyle’s law. Thus option 2 is incorrect.
• Faraday law is related to electromagnetic induction. Thus option 3 is correct.
• The volume remaining constant, the pressure of a given mass of a gas is directly proportional to its absolute temperature. This is the statement of Gay-Lussac’s law or pressure law. Thus option 4 is incorrect.

From kinetic theory of gases, the pressure P exerted by an ideal gas of density ρ and rms velocity of its gas molecules C is given by

Mean kinetic energy of translation per unit volume of the gas is

On dividing equations (1) and (2), we get