You have two gas-filled balloons, one containing He and the other H2. The H2 balloon is twice the size of the He balloon (let the He balloon have a volume of 1 -L and the H2 balloon. a volume of 2 L). The pressure of gas in the H2 balloon is 1 atm while that in the He balloon is 2 atm. The H2 balloon is outside in the snow (-1.11oC) while the He balloon is inside a warm building (21.1oC).
a) Which balloon contains the greater number of molecules? Show calculation.
b) Which balloon contains the greater mass of gas? Show calculation.
PV = nRT. Substitute and solve for n = number of moles. Convert to molecules remembering that 1 mol has 6.02E23 molecules.
b) n = grams/molar mass. You know n and molar mass. solve for grams and compare.
Ok so for the first part I got x=0.08969 for H2 and x=0.082 for He. but how do I convert to molecules?
Working on the second part now
ok so for the second part this is what I did.
0.082=x/4=0.328g
0.08969=x/2=0.179g
I feel like I have done something wrong though
First part b. No, you didn't do anything wrong. I agree with the 0.179 for g H2 gas. I have 0.331 g for He probably because I used 0.0828 for moles. I think you rounded that or just didn't read the last digit from your calculator.
Also, on moles H2, I obtained 0.08959. I used 0.08206 for R and 273.15+(-1.11) for T.
For a part, remember that 1 mol of molecules has 6.02E23 molecules. Just convert with that factor.
To find the number of molecules in each balloon, we can first use the Ideal Gas Law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
Let's start with the He balloon inside the warm building:
a) To find the number of molecules in the He balloon:
- The volume of the He balloon is given as 1 L.
- The pressure of gas in the He balloon is given as 2 atm.
- The temperature inside the warm building is given as 21.1°C.
First, we need to convert the temperature to Kelvin:
T = 21.1 + 273.15 = 294.25 K
Now, let's solve for the number of moles of He:
PV = nRT
(2 atm)(1 L) = n(0.0821 L·atm/(mol·K))(294.25 K)
2 = n(0.0821 L·atm/(mol·K))(294.25 K)
2 = 24.19247 n
n = 2 / 24.19247
n = 0.0824 moles
Since 1 mole contains 6.022 x 10^23 molecules (Avogadro's number), the number of molecules in the He balloon is:
Number of molecules = 0.0824 moles x 6.022 x 10^23 molecules/mole
Number of molecules = 4.95 x 10^22 molecules
Now, let's move on to the H2 balloon outside in the snow:
b) To find the number of molecules in the H2 balloon:
- The volume of the H2 balloon is given as 2 L.
- The pressure of gas in the H2 balloon is given as 1 atm.
- The temperature outside in the snow is given as -1.11°C.
First, we need to convert the temperature to Kelvin:
T = -1.11 + 273.15 = 272.04 K
Now, let's solve for the number of moles of H2:
PV = nRT
(1 atm)(2 L) = n(0.0821 L·atm/(mol·K))(272.04 K)
2 = n(0.0821 L·atm/(mol·K))(272.04 K)
2 = 22.351564 n
n = 2 / 22.351564
n = 0.0895 moles
The number of molecules in the H2 balloon is:
Number of molecules = 0.0895 moles x 6.022 x 10^23 molecules/mole
Number of molecules = 5.39 x 10^22 molecules
Therefore, the H2 balloon contains a greater number of molecules.
To find the mass of gas in each balloon, we need to use the molar mass of each gas:
- The molar mass (MM) of He is 4.003 g/mol.
- The molar mass (MM) of H2 is 2.016 g/mol.
The mass of gas in the He balloon is:
Mass of He = n x MM
Mass of He = 0.0824 moles x 4.003 g/mol
Mass of He = 0.329 g
The mass of gas in the H2 balloon is:
Mass of H2 = n x MM
Mass of H2 = 0.0895 moles x 2.016 g/mol
Mass of H2 = 0.180 g
Therefore, the He balloon contains a greater mass of gas.