Help-I'm really confused-The barometric pressure in my area is 1014 and the temperature is 61 degrees farhenheit. I am suppose to have an imaginary balloon that contains 22 grams of carbon dioxide. Calculate the volume in liters of the balloon using the gas law constant. Please help-this is just an extra credit question-but I do need help
1014 WHAT? Convert, whatever unit that is, to atmospheres.
Convert 61 F to degrees C, then convert to Kelvin.
Use PV = nRT to solve for V.
I forgot to say 1014 millibars-so how do I convert millibars to atm for my problem
Thank you
Sure! To calculate the volume of the balloon using the gas law constant, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atmospheres (convert barometric pressure to atmospheres if necessary)
V = volume in liters (what we need to calculate)
n = moles of gas (calculate using the mass and molar mass)
R = gas constant = 0.0821 L*atm/(mol*K)
T = temperature in Kelvin (convert Fahrenheit to Kelvin if necessary)
Let's break down the process step by step:
1. Convert the barometric pressure from millibars to atmospheres:
Since 1 bar = 1.01325 atm, we can calculate the pressure in atmospheres by dividing 1014 by 1013.25:
Barometric pressure in atmospheres = 1014 / 1013.25 = 1.00074 atm
2. Convert the temperature from Fahrenheit to Kelvin:
To convert Fahrenheit to Celsius, we can use the formula: C = (F - 32) * 5/9
Then, to convert Celsius to Kelvin: K = C + 273.15
Temp in Celsius = (61 - 32) * 5/9 ≈ 16.11°C
Temp in Kelvin = 16.11 + 273.15 ≈ 289.26 K
3. Calculate the number of moles of carbon dioxide in the balloon:
To calculate the number of moles, we need to know the molar mass of carbon dioxide (CO2), which is approximately 44 g/mol.
Moles of CO2 = mass of CO2 / molar mass of CO2
Moles of CO2 = 22 g / 44 g/mol = 0.5 mol
4. Plug the values into the ideal gas law equation PV = nRT:
P = 1.00074 atm (from Step 1)
V = ? (what we're solving for)
n = 0.5 mol (from Step 3)
R = 0.0821 L*atm/(mol*K)
T = 289.26 K (from Step 2)
(1.00074 atm) * V = (0.5 mol) * (0.0821 L*atm/(mol*K)) * (289.26 K)
5. Solve for V by dividing both sides of the equation by the pressure (1.00074 atm):
V = (0.5 mol * 0.0821 L*atm/(mol*K) * 289.26 K) / 1.00074 atm
V ≈ 11.13 L
Therefore, the volume of the imaginary balloon would be approximately 11.13 liters.