The gaseous product of a reaction is collected in a 25.0-L container at 27 C. The pressure in the container is 216 kPa, and the gas has a mass of 96.0 g. What is the molar mass of the gas?

To determine the molar mass of the gas, we can use the ideal gas law equation:

PV = nRT

where:
P = pressure in atmosphere (convert 216 kPa to atm)
V = volume in liters (25.0 L)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin (convert 27ºC to Kelvin)

First, let's convert the pressure from kilopascals to atmospheres:

1 atm = 101.325 kPa

So, the pressure in atmospheres is:
216 kPa / 101.325 kPa/atm = 2.13 atm

Next, let's convert the temperature from Celsius to Kelvin:

T(K) = T(°C) + 273.15
T(K) = 27°C + 273.15 = 300.15 K

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

n = PV / RT

n = (2.13 atm) * (25.0 L) / (0.0821 L·atm/(mol·K) * 300.15 K)

n = 21.78 moles

Finally, to calculate the molar mass (M) of the gas:

M = mass / n

M = 96.0 g / 21.78 mol

M = 4.41 g/mol

Therefore, the molar mass of the gas is 4.41 g/mol.

To determine the molar mass of the gas, we'll need to use the ideal gas law equation, which is:

PV = nRT

Where:
- P is the pressure of the gas in Pascal (Pa)
- V is the volume of the container in cubic meters (m^3)
- n is the number of moles of the gas
- R is the ideal gas constant, which is approximately 8.314 J/(mol·K)
- T is the temperature of the gas in Kelvin (K)

However, the given values for pressure, volume, and temperature are in different units. Let's convert them into the appropriate unit:

Given:
- Pressure (P) = 216 kPa
- Volume (V) = 25.0 L
- Temperature (T) = 27 °C

We need to convert the temperature from Celsius to Kelvin by adding 273.15:
T = 27 °C + 273.15 = 300.15 K

We also need to convert the volume from liters to cubic meters by dividing by 1000:
V = 25.0 L / 1000 = 0.025 m^3

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

(P * V) = (n * R * T)

n = (P * V) / (R * T)

Let's calculate it:

n = (216,000 Pa * 0.025 m^3) / (8.314 J/(mol·K) * 300.15 K)

Simplifying the equation:
n = 0.18 mol

Now that we know the number of moles, we can find the molar mass of the gas by dividing the mass (given as 96.0 g) by the number of moles:

Molar mass = mass / moles

Molar mass = 96.0 g / 0.18 mol

Calculating the molar mass:
Molar mass = 533.33 g/mol

Therefore, the molar mass of the gas is 533.33 g/mol.

Use PV = nRT to solve for n = number of moles. Then moles = grams/molar mass and solve for molar mass.

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