How many moles of helium are contained in a 5.00-L canister at 101 kPa and 30.0 degrees Celsius? I don't understand how to get the answer. My teacher didn't explain the work she just gave me the answer.
Use PV = nRT
P must be in atmospheres. 101 kPa = 1 atom (almost 1.00, technically it is 101/101.326 = ??. I don't know what your teacher recommended.)
V = 5.00 L
R = 0.08206 L*atm/mol*K
T = 30.0 C which must be converted to Kelvin.
K = 273 + 30 = ??
Substitute these values into PV = nRT an solve for n.
Using 101.325 kPa = 1 atm I obtained an answer of 0.200 moles.
0.200
To determine the number of moles of helium gas in the canister, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure in atmospheres (convert from kPa if necessary)
V = volume in liters
n = number of moles
R = gas constant (0.0821 L·atm/mol·K)
T = temperature in Kelvin (convert from Celsius if necessary)
To solve for the number of moles (n), rearrange the equation and plug in the given values:
n = PV / RT
First, convert the given pressure of 101 kPa to atmospheres:
1 atm = 101.325 kPa
101 kPa / 101.325 kPa/atm = 0.996 atm
Next, convert the given temperature of 30.0 degrees Celsius to Kelvin:
T(K) = T(°C) + 273
T(K) = 30 + 273 = 303 K
Now, you can substitute the values into the equation:
n = (0.996 atm) x (5.00 L) / (0.0821 L·atm/mol·K) x (303 K)
Simplifying the equation:
n = 0.20023 mol
Therefore, there are approximately 0.200 moles of helium in the canister.
To calculate the number of moles of helium in a given container, you need to use the ideal gas law equation:
PV = nRT
Where:
P is the pressure (in units of Pa or atm)
V is the volume (in units of liters)
n is the number of moles
R is the ideal gas constant (8.314 J/(mol·K))
T is the temperature (in units of Kelvin)
Firstly, we need to convert the given values to the appropriate units. The pressure is already given in kPa, but we need to convert it to Pa. The volume is given in liters, which is suitable for the equation. However, the temperature also needs to be converted to Kelvin.
To convert from degrees Celsius to Kelvin, you add 273.15 to the Celsius value. So, in this case, the temperature is 30.0 + 273.15 = 303.15 K.
Now, substitute the values into the equation:
(101 kPa) * (5.00 L) = n * (8.314 J/(mol·K)) * (303.15 K)
Simplifying:
505 kPa·L = n * 2499.74 J/K
Rearranging the equation to solve for moles (n):
n = (505 kPa·L) / (2499.74 J/K)
Now, we need to convert kPa·L to J by multiplying by the conversion factor of 1000 J/1 kJ:
n = (505 kPa·L) / (2499.74 J/K) * (1 kJ/1000 J)
Finally, we can calculate the moles of helium:
n = (505 kPa·L * 1 kJ/1000 J) / (2499.74 J/K)
n ≈ 0.202 mol
Therefore, there are approximately 0.202 moles of helium in the 5.00-L canister at 101 kPa and 30.0 degrees Celsius.