If a balloon filled with carbon dioxide has occupies a volume of 31 L at STP, what is the mass of the gas?
Use PV = nRT and solve for n = number of mols. Then n = grams/molar mass. You know n and molar mass, solve for grasm.
Another way to do it is to recognize that at STP 1 mol of a gas occupies 22.4 L. So mol = 31/22.4 and that x molar mass = grams.
Well, if it's filled with carbon dioxide, then it explains why the balloon looks so serious all the time. Now, let's calculate its mass. At STP (Standard Temperature and Pressure), the molar volume of any gas is 22.4 liters. So, we can start by finding the number of moles of carbon dioxide using the ideal gas law. But before that, let me prepare my clown calculator... *honk honk* Okay, let's do this!
We have:
Volume (V) = 31 liters
Molar volume (V_m) = 22.4 liters/mol
By rearranging the ideal gas law equation, we get:
n = PV / RT
Where:
P = Pressure = 1 atm (at standard pressure)
R = Ideal gas constant = 0.0821 L·atm/(mol·K)
T = Temperature = 273 K (at standard temperature)
Now, we can calculate:
n = (1 atm) * (31 L) / (0.0821 L·atm/(mol·K) * 273 K)
*clown calculator noises*
After a series of interesting calculations, we find that the number of moles (n) is approximately 1.22 moles.
Now, the molar mass of carbon dioxide is roughly 44 grams/mol. So, the mass of the gas in the balloon would be:
Mass = n * molar mass = 1.22 moles * 44 g/mol
*drumroll please*
And that gives us a mass of around 53.68 grams. Voila!
To calculate the mass of the gas, we need to use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature.
At STP (Standard Temperature and Pressure):
- Temperature (T) = 273 K
- Pressure (P) = 1 atm
- Ideal gas constant (R) = 0.0821 L·atm/(mol·K)
Given:
- Volume (V) = 31 L
First, let's calculate the number of moles of gas (n) using the ideal gas law equation:
PV = nRT
n = (PV) / (RT)
n = (1 atm x 31 L) / (0.0821 L·atm/(mol·K) x 273 K)
n ≈ 1.21 moles
Now, to calculate the mass of the gas, we need to know the molar mass (M) of carbon dioxide (CO2), which is:
M(CO2) = 12.01 g/mol (mass of C) + 2 x 16.00 g/mol (mass of O)
M(CO2) ≈ 44.01 g/mol
Finally, we can calculate the mass of the gas by multiplying the number of moles by the molar mass:
Mass = n x M(CO2)
Mass = 1.21 moles x 44.01 g/mol
Mass ≈ 53.27 g
Therefore, the mass of the gas in the balloon is approximately 53.27 grams.
To find the mass of the gas, we need to use the ideal gas law equation, which is PV = nRT, where:
- P represents the pressure of the gas in atmospheres (atm),
- V represents the volume of the gas in liters (L),
- n represents the number of moles of the gas,
- R is the ideal gas constant, which is 0.0821 L·atm/(mol·K), and
- T represents the temperature in Kelvin (K).
Since we are given the volume (V) of the gas at STP (Standard Temperature and Pressure), which is 31 L, we can rearrange the ideal gas law equation to solve for the number of moles (n) of the gas:
n = PV / RT
Now, let's plug in the known values into the equation:
- P = 1 atm (at STP),
- V = 31 L,
- R = 0.0821 L·atm/(mol·K), and
- T = 273.15 K (at STP).
n = (1 atm) * (31 L) / (0.0821 L·atm/(mol·K) * 273.15 K)
Now, let's calculate the value of n:
n = 1.192 mol
Therefore, the number of moles of carbon dioxide gas in the balloon is approximately 1.192 mol.
To find the mass of the gas, we need to multiply the number of moles by the molar mass of carbon dioxide (CO2). The molar mass of CO2 is calculated by adding the atomic masses of carbon (C) and two oxygen (O) atoms:
C: 12.01 grams/mole
O: 16.00 grams/mole
Molar mass of CO2 = (12.01 g/mol) + (16.00 g/mol) + (16.00 g/mol) = 44.01 g/mol
Now, we can calculate the mass (m) of the gas:
m = n * Molar mass of CO2
m = (1.192 mol) * (44.01 g/mol)
m ≈ 52.48 g
Therefore, the mass of the carbon dioxide gas in the balloon is approximately 52.48 grams.