An ideal gas at 200.0 k and 1.50 atm pressure is heated to 1000.0 k and kept at 1.50 atm pressure. which of the statements below are true? if they are not true, be sure to explain how you know.

i. the root mean square speed of the molecules increases by a factor of five.

ii. the average molecular kinetic energy increases by a factor of twenty–five.

iii. the collision frequency with a unit area of container wall increases.

iv. the average molecular kinetic energy increases by a factor of five

expert answer

Ony statement IV is true.

The average molecular kinetic energy increases by a factor of five

Explanation:

Step 1: Data given

Initial temperature of the gas = 200.00 K

Final temperature = 1000.0 K

Pressure = constant = 1.50 atm

I. The root mean square speed of the molecules increases by a factor of five.

The root-mean-square speed  u (rms ) of a gas  is given by the following equation: √(3RT/MM)

with R = universal gasconstant

with T = absolute temperature in Kelvin

with MM = Molar mass

We can call 3R/MM = the constant k

u(rms1) can be given as:

√(kT)

When the temperature is 5x the original temperature

u(rms2) = √(5kT)

u(rms2)/u(rms1) = √(5kT) /√(kT) = √5

So when the temperature increases wit ha factor 5, the speed increases with a factor √5

This statement is false.

II. The average molecular kinetic energy increases by a factor of twenty–five.

If the temperature of a gas is doubled, the average kinetic energy of its molecules is doubled

If the temperature of a gas increases by a factor 5, the average kinetic energy of its molecules increases by a factor 5 AND NOT 25.

This statement is false.

III. The collision frequency with a unit area of container wall increases.

 ⇒ Boyle's law says: If the gas volume is decreased, the container wall area decreases and the molecule-wall collision frequency increases.

This statement is false.

IV. The average molecular kinetic energy increases by a factor of five

If the temperature of a gas is doubled, the average kinetic energy of its molecules is doubled

If the temperature of a gas increases by a factor 5, the average kinetic energy of its molecules increases by a factor 5

This statement is true.

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