You have a 22L cylinder of helium at a pressure of 150atm and a temperature of 31C. How many ballons can you fill, each with a volume of 5.0L, on a day when the atmospheric pressure is 755mmHg and the temperature is 22C?
Use PV = nRT to calculate n, number of moles in the cylinder of He.
Plug n into PV=nRT under the new conditions to determine the volume at the new conditions. The number balloons = new volume x (1 balloon/5.0L) = ??
To find out how many balloons can be filled, we'll need to use the ideal gas law equation, which is:
PV = nRT
Where:
P = pressure
V = volume
n = moles of gas
R = ideal gas constant (0.0821 L.atm/mol.K)
T = temperature
First, we need to convert the given atmospheric pressure to atm because the given helium pressure is in atm.
Given:
Atmospheric pressure = 755 mmHg
Convert 755 mmHg to atm using the conversion factor 1 atm = 760 mmHg:
Atmospheric pressure (in atm) = 755 mmHg * (1 atm / 760 mmHg) = 0.9934 atm (rounded to four decimal places)
Now, we can calculate the number of moles of helium gas in the cylinder:
n = (PV) / (RT)
Given:
P = 150 atm (pressure of helium)
V = 22 L (volume of helium)
T = 31°C (temperature of helium)
Convert the temperature from Celsius to Kelvin:
T = 31°C + 273.15 = 304.15 K (rounded to two decimal places)
Now, plug in the values into the equation:
n = (150 atm * 22 L) / (0.0821 L.atm/mol.K * 304.15 K)
n ≈ 10.012 moles (rounded to three decimal places)
Since each balloon requires a volume of 5.0 L, we need to divide the total volume of the helium by the volume of each balloon to find the number of balloons that can be filled:
Number of balloons = Total volume of helium / Volume of each balloon
Number of balloons = 22 L / 5.0 L ≈ 4.4 balloons
Therefore, you can fill approximately 4 balloons (rounded to the nearest whole number) with the given conditions.