How many moles of gas are in a 20 liter scuba canister is 300k and pressure is 200 atm
To find the number of moles of gas in a given scuba canister, we can use the ideal gas law equation: PV = nRT, where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin.
First, we need to convert the given temperature from degrees Celsius (°C) to Kelvin (K). The conversion formula is K = °C + 273.15.
Given:
- Volume (V) = 20 liters
- Pressure (P) = 200 atm
- Temperature (T) = 300 K
We can rearrange the ideal gas law equation to solve for n:
n = (PV)/(RT)
The ideal gas constant, R, is typically expressed as 0.0821 L·atm/(mol·K).
Substituting the given values into the equation:
n = (200 atm * 20 L) / (0.0821 L·atm/(mol·K) * 300 K)
Simplifying:
n = (4000 L·atm) / (24.63 L·atm/(mol·K))
Finally, we can calculate the number of moles:
n = 162.2043 moles (rounded to four decimal places)
Therefore, there are approximately 162.2043 moles of gas in the 20 liter scuba canister when the temperature is 300 K and the pressure is 200 atm.
To determine the number of moles of gas in a scuba canister, you can use the ideal gas law equation:
PV = nRT
Where:
P = Pressure of the gas (in atm)
V = Volume of the gas (in liters)
n = Number of moles of gas
R = Ideal gas constant (0.0821 L.atm/mol.K)
T = Temperature of the gas (in Kelvin)
Let's plug in the values given in the question:
P = 200 atm
V = 20 liters
T = 300 K
Now, rearrange the equation to solve for n:
n = PV / RT
Substituting the values:
n = (200 atm * 20 L) / (0.0821 L.atm/mol.K * 300 K)
n = 4000 L.atm / (24.63 L.atm/mol.K)
n ≈ 162.35 mol
Therefore, there are approximately 162.35 moles of gas in the 20 liter scuba canister at a temperature of 300 K and pressure of 200 atm.