how many moles of gas are contained in a 50.0L cylinder at a pressure of 100.0 atm and a pressure of 35 C?
Use PV = nRT and don't forget to convert 35 C to Kelvin. Solve for n. You made a typo. I'm sure you meant a temperature of 35 C.
To determine the number of moles of gas in a given sample, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atmospheres)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the given temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
So, T = 35 °C + 273.15 = 308.15 K
Plugging the given values into the ideal gas law equation:
(100.0 atm)(50.0 L) = (n)(0.0821 L·atm/(mol·K))(308.15 K)
Simplifying:
5000 atm·L = 25.41641 n
Now, we isolate the number of moles (n):
n = 5000 atm·L / 25.41641 L·atm/(mol·K)
n ≈ 196.54 moles
Therefore, there are approximately 196.54 moles of gas contained in the 50.0L cylinder at a pressure of 100.0 atm and a temperature of 35 °C.
To calculate the number of moles of gas in a cylinder, you can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature (in Kelvin)
First, let's convert the temperature from Celsius to Kelvin:
T(K) = T(°C) + 273.15
T(K) = 35 + 273.15
T(K) = 308.15 K
Now we can plug in the values into the ideal gas law equation:
PV = nRT
(100.0 atm) * (50.0 L) = n * (0.0821 L·atm/(mol·K)) * (308.15 K)
5000 = n * (0.0821 L·atm/(mol·K)) * (308.15 K)
Simplifying the equation, we get:
n = (5000) / ((0.0821) * (308.15))
n ≈ 1.971 moles
Therefore, there are approximately 1.971 moles of gas in the 50.0 L cylinder at a pressure of 100.0 atm and a temperature of 35°C.