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 <u>factor √5</u>
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.
