At a pressure of 103 kPa and a temperature of 22oC, 52.9 g of a certain gas has a volume of 31.5 L. What is the identity of this gas?

how do you find the molar mass

To determine the identity of the gas, we can use the ideal gas law, which states that:

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)

First, we need to convert the given pressure to atm and the temperature to Kelvin:

Given:
Pressure = 103 kPa
Temperature = 22 °C

1 atm = 101.325 kPa
So, the pressure in atm = 103 kPa / 101.325 kPa/atm = 1.017 atm

To convert temperature to Kelvin:
Temperature in Kelvin = 22 °C + 273.15 °K = 295.15 K

Now we have the following values:
P = 1.017 atm
V = 31.5 L
n = ?
R = 0.0821 L·atm/mol·K
T = 295.15 K

Next, rearrange the ideal gas law equation to solve for the number of moles (n):

n = (PV) / (RT)

Plugging in the values:

n = (1.017 atm × 31.5 L) / (0.0821 L·atm/mol·K × 295.15 K)
n ≈ 1.309

Therefore, the number of moles is approximately 1.309 moles.

To find the molar mass of the gas, we need to calculate the mass of the gas. We know the number of moles and the mass (52.9 g), so we can calculate the molar mass.

Molar mass = mass / number of moles
Molar mass = 52.9 g / 1.309 mol
Molar mass ≈ 40.42 g/mol

Now we need to find the gas with a molar mass of approximately 40.42 g/mol. Looking at the periodic table, one gas that has a molar mass close to this value is argon (Ar), which has a molar mass of 39.95 g/mol.

Therefore, the identity of the gas is likely argon (Ar).

To determine the identity of a gas, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.

First, let's convert the given temperature from Celsius to Kelvin.

T (Kelvin) = T (Celsius) + 273.15
T (Kelvin) = 22 + 273.15 = 295.15 K

Now we can rearrange the ideal gas law equation to solve for the number of moles (n):

n = PV / RT

n = (103 kPa)(31.5 L) / (0.0821 L·atm/(mol·K))(295.15 K)

Here, we use the value of the ideal gas constant in units suitable for the given values, which is 0.0821 L·atm/(mol·K).

Calculating the value for n:

n = (103 kPa)(31.5 L) / (0.0821 L·atm/(mol·K))(295.15 K)
n ≈ 1.39 mol

Now we can determine the molar mass of the gas using the equation:

Molar mass (grams/mol) = mass (grams) / moles

Molar mass (grams/mol) = 52.9 g / 1.39 mol
Molar mass ≈ 38.13 g/mol

To identify the gas, we can use the molar mass to compare it with the molar masses of known gases. In this case, the molar mass of approximately 38.13 g/mol can correspond to a variety of gases. You would need additional information to narrow down the possibilities and identify the specific gas.

Use PV = nRT

I would change 103 kPa to atmospheres, change 22 C to Kelvin (273 + C = Kelvin), and plug in V, solve for n = number of moles.
Then number of moles = grams/molar mass.
You know moles, you know grams, solve for molar mass, then look on the periodic table to find the name of the element. (Note: I have assumed that this is a gas element, it COULD be CO2 or some other gas. But find the molar mass and then we can figure out what to do if it isn't an element.)