The density of a gas is 1.96 g L–1 at 1.00 atm and 0
°C. What is the density of this gas at 0.855 atm and 25.0
C?
Two ways to do this. The long way, but easier to explain, and the short way but harder to explain. The long way first:
The general gas formula can be modifed to
P*M = dRT where M is molar mass and d is density in g/L. Substitute into that and solve for M. Then use the same equation, substitute the new conditions and solve for the new density.
Shorter way.
1.96 x (pres factor) x (Temp factor) =
1.96 g/L x (0.855/1) x (273/298) = ?
How does the shorter way work?
P factor. P decreases therefore L increases and density gets smaller so the factor must be less than 1 which makes the small number go in the numerator.
T factor. T increases from 273 to 298, L must increase, larger L means smaller density so the T factor must be less than 1 which makes the small number go on top.
1.8
I'm sorry, I need more information in order to help you. What is your question?
Well, let me calculate that for you, but while I do that, let me ask you, have you ever noticed that gases have a tendency to "float" around? I mean, they don't settle down like some of my dad jokes. They just zip around, being all free and airy. It's like they're always looking for a gas escape route.
To determine the density of a gas at different conditions, you can use the ideal gas law equation and apply the concept of molar volume. The ideal gas law equation is as follows:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in L)
n = number of moles
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
To find the density of the gas, we can rearrange the ideal gas law equation as follows:
density (d) = (molar mass of the gas) / (molar volume)
Step 1: Calculate the molar volume at the given conditions.
To convert the given temperature of 0°C to Kelvin:
T1 = 0°C + 273.15 = 273.15 K (since 0°C is equivalent to 273.15 K)
The given conditions are:
P1 = 1.00 atm
T1 = 273.15 K
d1 = 1.96 g/L
Using the ideal gas law equation, we can solve for the molar volume (V1):
V1 = (n * R * T1) / P1
Step 2: Calculate the number of moles (n) at the given conditions:
We know the mass, molar mass, and volume. From that, we can calculate the number of moles (n):
n = (mass) / (molar mass)
= (density * volume) / (molar mass)
= (d * V1) / (molar mass)
Step 3: Calculate the molar volume (V2) at the new conditions:
For the new conditions, we have:
P2 = 0.855 atm
T2 = 25.0°C + 273.15 = 298.15 K (since 25.0°C is equivalent to 298.15 K)
Using the ideal gas law equation, we can solve for the molar volume (V2):
V2 = (n * R * T2) / P2
Step 4: Calculate the density at the new conditions:
Using the rearranged equation for density:
density (d2) = (molar mass) / (molar volume)
d2 = (molar mass) / V2
Now you can substitute V2 using the calculated value and solve for d2.
It is essential to know the molar mass of the gas to obtain the final answer.