An unknown amount of gas occupies 30.0 L at 2.1 atm and 298K. How many moles does the sample contain? What is the mass if the gas is helium? What is the mass if the gas is argon?

To find the number of moles in a gas sample, we can use the ideal gas law equation:

PV = nRT

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

Let's calculate the number of moles using this formula:

Given:
Pressure (P) = 2.1 atm
Volume (V) = 30.0 L
Temperature (T) = 298 K

First, we rearrange the formula to solve for n:

n = PV / RT

Now, we substitute the given values in the formula:

n = (2.1 atm * 30.0 L) / (0.0821 L.atm/mol.K * 298 K)

n = 1.90 moles (rounded to two decimal places)

So, the sample contains approximately 1.90 moles of gas.

To calculate the mass of the gas, we need to know its molecular weight. Given that the options are helium (He) and argon (Ar), we can find their respective molecular weights.

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

The molar mass of argon (Ar) is approximately 39.95 g/mol.

To calculate the mass of the gas sample, we can use the formula:

Mass = number of moles * molar mass

For helium:

Mass of helium = 1.90 moles * 4.00 g/mol

Mass of helium = 7.60 g (rounded to two decimal places)

So, if the gas is helium, the mass of the sample would be approximately 7.60 grams.

For argon:

Mass of argon = 1.90 moles * 39.95 g/mol

Mass of argon = 75.91 g (rounded to two decimal places)

So, if the gas is argon, the mass of the sample would be approximately 75.91 grams.

To calculate the number of moles in the gas sample, we can use the Ideal Gas Law equation:

PV = nRT

where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)

1. To find the number of moles:

n = PV / RT

Substituting the given values:

n = (2.1 atm * 30.0 L) / (0.0821 L·atm/(mol·K) * 298K)
n = 2.55 moles (approximately)

Therefore, the gas sample contains approximately 2.55 moles.

2. To find the mass if the gas is helium (He):

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

The mass of the gas sample (in grams) can be calculated using the formula:

Mass = number of moles * molar mass

Mass of helium = 2.55 moles * 4.00 g/mol
Mass of helium = 10.20 grams

Therefore, if the gas in the sample is helium, its mass would be approximately 10.20 grams.

3. To find the mass if the gas is argon (Ar):

The molar mass of argon (Ar) is approximately 39.95 g/mol.

Using the same formula:

Mass of argon = 2.55 moles * 39.95 g/mol
Mass of argon = 101.97 grams

Therefore, if the gas in the sample is argon, its mass would be approximately 101.97 grams.