A sample of methane (CH4) gas contains a small amount of helium. Calculate the volume percentage of helium if the density of the sample is 0.70902 g/L t 273K and 1.00 atm.

I know that the sample is at STP and that the 1 mole of gas under these conditions occupies 22.4L, but how do I use the density to find the fractional volumes that each gas inhabits?

The general gas formula of PV = nRT can be rearranged for molar mass of

P*M = density*RT
M = dRT/P = about 15.9 but you need to do it for a more accurate answer.
Then let X = fraction CH4
and 1-X = fraction He
Then molar mass CH4*X + molar mass He*(1-x) = molar mass from above.

Solve for X (and 1-X if needed) and convert to percent.
Note: Since the density is contains 5 significant figures I would use R = 0.082057 and use at least 5 places for CH4 and He AND I would carry everything out to 6 places before rounding.
I obtained about 98.7% but that's only a close estimate.

Thanks

Well, I must say, this is one gas-tastic question! Let's dive right into it, shall we?

To find the volume percentage of helium in the sample, we'll need to utilize a little bit of gas law magic. First, we need to determine the molar mass of methane (CH4) and helium (He).

The molar mass of methane (CH4) is calculated as follows:
Molar mass of methane (CH4) = (C's molar mass) + (4 x H's molar mass)
= (12.01 g/mol) + (4 x 1.01 g/mol)
= 16.05 g/mol

The molar mass of helium (He) is simply 4.00 g/mol.

Now, we can use the ideal gas law equation: PV = nRT

Where:
P is the pressure (1.00 atm)
V is the volume (unknown)
n is the number of moles (unknown)
R is the ideal gas constant (0.0821 L.atm/mol.K)
T is the temperature in Kelvin (273 K)

From the density given (0.70902 g/L), we can convert it to molar mass:
0.70902 g/L x (1 mol/16.05 g) = 0.04414 mol/L

Using the ideal gas law equation, we can rearrange it to solve for V (volume):
V = (nRT) / P
= (0.04414 mol/L x 0.0821 L.atm/mol.K x 273 K) / 1.00 atm
≈ 9.71 L

So, the sample occupies approximately 9.71 L.

To find the volume percentage of helium, we need to know the volume of helium in the sample. Given that the sample is at STP and 1 mole of gas occupies 22.4 L, we can calculate:
Volume of helium = (number of moles of helium) x (molar volume at STP)
= (X mol) x (22.4 L/mol)

As we don't know the amount of helium yet, let's call it X. Now, we replace the values we know into the equation:
9.71 L = X mol x 22.4 L/mol

Solving for X, we find:
X ≈ 0.434 moles of helium

Finally, to determine the volume percentage of helium, we use the following formula:
Volume percentage of helium = (Volume of helium / Total volume of sample) x 100%

Plugging in the values, we get:
(0.434 mol x 22.4 L/mol) / 9.71 L x 100%
≈ 1.00 % (rounded to two decimal places)

So, the volume percentage of helium in the sample is approximately 1.00%. Helium surely knows how to make us float with joy!

To calculate the volume percentage of helium in the sample, you can use the molar mass and density of methane (CH4) and helium (He).

1. Determine the molar mass of methane (CH4) and helium (He):

- Molar mass of methane (CH4) = 12.01 g/mol (carbon) + 4 * 1.01 g/mol (hydrogen) = 16.04 g/mol
- Molar mass of helium (He) = 4.00 g/mol

2. Calculate the volume of one mole of the sample at STP:

- 1 mole of gas at STP occupies 22.4 L

3. Calculate the densities of methane (CH4) and helium (He):

- For methane (CH4), given density = 0.70902 g/L
=> Mass of methane = density * volume = 0.70902 g/L * 22.4 L = 15.85 g
=> Moles of methane (CH4) = mass / molar mass = 15.85 g / 16.04 g/mol = 0.988 mol

- For helium (He), the density is not given, but since the amount of helium is small, let's assume it doesn't contribute significantly to the density. Therefore, we can consider the density of the mixture to be the same as the density of methane.

4. Calculate the volume of helium:

- Volume of helium = Total volume - Volume of methane = 22.4 L - 22.4 L = 0 L (since we assumed helium doesn't contribute significantly to the density)

5. Calculate the volume percentage of helium:

- Volume percentage of helium = (Volume of helium / Total volume) * 100
= (0 L / 22.4 L) * 100
= 0%

Therefore, based on the given information and assumptions, the volume percentage of helium in the sample is 0%.

To find the volume percentage of helium in the sample, we need to first determine the volumes of methane and helium in the sample. To do this, we can use their respective molar masses and the given density.

First, let's calculate the molar mass of methane (CH4):
- Carbon (C): 12.01 g/mol
- Hydrogen (H): 1.008 g/mol (there are four hydrogens in methane)
Molar mass of CH4 = (12.01 g/mol) + (4 * 1.008 g/mol) = 16.04 g/mol

Next, let's calculate the molar mass of helium (He):
Molar mass of He = 4.0026 g/mol

Now, we can use the fact that 1 mole of gas at STP occupies 22.4 L to find the volumes of methane and helium in the sample.

Let's assume we have a sample volume of V liters. From the density, we know that the sample mass is 0.70502 * V grams.

The number of moles of methane in the sample can be calculated by dividing the sample mass by the molar mass of methane:
Moles of CH4 = (0.70902 * V grams) / (16.04 g/mol)

Similarly, the number of moles of helium in the sample can be calculated by dividing the sample mass by the molar mass of helium:
Moles of He = (0.70902 * V grams) / (4.0026 g/mol)

To find the volume of methane, we can use the fact that 1 mole of gas at STP occupies 22.4 L:
Volume of CH4 = (Moles of CH4) * 22.4 L

Similarly, the volume of helium is:
Volume of He = (Moles of He) * 22.4 L

Now, to find the volume percentage of helium, we divide the volume of helium by the total volume of the sample (V liters) and multiply by 100:
Volume percentage of He = (Volume of He / V) * 100

By substituting the appropriate values into these equations, you can calculate the volume percentage of helium in the methane gas sample.