Determine the mass of CO2 gas that has a volume of 7.10 L at a pressure of 1.11 atm and a temperature of 31.0°C.

3

Why did the CO2 gas go on a diet?

Because it wanted to determine its mass!

But don't worry, I have the mathematical recipe to calculate it for you. First, let's convert the temperature to Kelvin by adding 273.15:

T = 31.0°C + 273.15 = 304.15 K

Now, let's use the ideal gas law to find the number of moles of CO2 gas:

PV = nRT

Where:
P = pressure = 1.11 atm
V = volume = 7.10 L
n = number of moles (unknown)
R = ideal gas constant = 0.0821 L·atm/(mol·K)
T = temperature = 304.15 K

Solving for n:

n = PV / RT

n = (1.11 atm)(7.10 L) / (0.0821 L·atm/(mol·K))(304.15 K)

Now, let me do the math... drumroll, please!

n ≈ 0.334 moles

Finally, to determine the mass of CO2 gas, we need to use its molar mass, which is approximately 44.01 g/mol.

m = n * molar mass

m = (0.334 moles) * (44.01 g/mol)

Voila! The mass of CO2 gas with a volume of 7.10 L at a pressure of 1.11 atm and a temperature of 31.0°C is approximately 14.6 grams.

To determine the mass of CO2 gas, we can use the Ideal Gas Law equation: PV = nRT, where:

- P is the pressure of the gas in atm (1.11 atm)
- V is the volume of the gas in L (7.10 L)
- n is the number of moles of the gas (to be determined)
- R is the ideal gas constant (0.0821 L·atm/mol·K)
- T is the temperature in Kelvin (31.0°C = 31.0 + 273.15 = 304.15 K)

First, let's rearrange the Ideal Gas Law equation to solve for n:
n = (PV) / (RT)

Now, we can substitute the given values into the equation:
n = (1.11 atm * 7.10 L) / (0.0821 L·atm/mol·K * 304.15 K)

n ≈ 0.312 mol

The number of moles of CO2 gas is approximately 0.312 mol.

To find the mass, we need to use the molar mass of CO2. The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol.

So, the mass of CO2 can be calculated by multiplying the number of moles by the molar mass:
mass = n * molar mass
mass = 0.312 mol * 44.01 g/mol

mass ≈ 13.72 g

Therefore, the mass of CO2 gas with a volume of 7.10 L, pressure of 1.11 atm, and a temperature of 31.0°C is approximately 13.72 grams.

To determine the mass of CO2 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.

First, we need to convert the given values to the appropriate units:
- Pressure: 1.11 atm (already in the correct unit)
- Volume: 7.10 L (already in the correct unit)
- Temperature: 31.0°C
The ideal gas constant, R, is 0.0821 L·atm/(mol·K).

Step 1: Convert the temperature to Kelvin (K).
We know that Celsius and Kelvin temperatures are related by the equation: K = °C + 273.15.
So, the temperature in Kelvin would be 31.0 + 273.15 = 304.15 K.

Step 2: Calculate the number of moles (n).
Using the ideal gas law equation, we can rearrange it to solve for n:
n = PV / RT.

Plugging in the values:
n = (1.11 atm * 7.10 L) / (0.0821 L·atm/(mol·K) * 304.15 K)
n ≈ 0.324 mol.

Step 3: Calculate the mass of CO2 gas.
The molar mass of carbon dioxide (CO2) is approximately 44.01 g/mol.

Mass = n * molar mass
Mass ≈ (0.324 mol) * (44.01 g/mol)
Mass ≈ 14.26 g.

Therefore, the mass of CO2 gas with a volume of 7.10 L at a pressure of 1.11 atm and a temperature of 31.0°C is approximately 14.26 g.

Solve for the number of moles (n) using PV=nRT. R = 0.0821 liter·atm/mol·K, T= 31.0 +273K, P=1.11, V=7.10L. Rearrange the equation to give you n=PV/RT and plug in your values (n=[(1.11 atm)(7.10L)]/[(0.0821 liter·atm/mol·K)(31.0 +273.15K)]. Once you solve for the number of moles, divide n, by the molecular weight of CO2 (n/44.01 g/mol) which will give you the mass.