Remember that the equation for the ideal gas is:
P*V = n*R*T
Where:
P = pressure
V = volume
n = number of moles
R = constant of the ideal gases.
T = temperature.
1) If the pressure is held constant (we also assume n is constant, because usually, the number of moles does not change).
Then we can write
V = (n*R/P)*T
and (n*R/P) is a constant.
Then the above relation is a proportional relation.
So the correct option is C: The relationship is directly proportional, as temperature increases, volume increases in the same way.
2) If the pressure increases and the temperature is held constant, then the equation:
V = (n*R/P)*T
can be used.
Now the temperature is constant, so we can write this as
V = (n*R*T)/P
Where now (n*R*T) is a constant.
So now we have an inversely proportional relation, when P increases, the volume should decreases. And a decrease in volume happens because the molecules move closer together, so the correct option is C:
"an increase in pressure causes particles move closer together, decreasing the volume."
3) Now the volume is constant, then we can write:
P = (n*R/V)*T
Exact same thing as in the first case, this is a proportional relation, so if the temperature increases, also does the pressure.
The correct option is C again.
4) If the pressure decreases then temperature also decreases, as we saw above.
And as the temperature decreases, the volume increases, as we saw in point (2), then the correct option is D, i the pressure decreases, the volume increases.
5) We have two different gases with the same values of T, V, and P.
By the equation:
P*V = n*R*T
And knowing that R is a constant, we can see that n should also be the same value for both gases.
Then the molar volume of each gas, V/n, is also the same.
Finally, the only thing that can be different in the gases is the thing that does not appear in the equation, and that is density/mass. So we can conclude that the gasses have different masses (thus different density, as they have the same volume)
Then the correct option is B; the mass of each gas.
If you want to learn more, you can read:
brainly.com/question/8711877
