A compressed gas cylinder contains 1.00 into 1000 g argon gas . the pressure inside the cylinder is 2050 psi at a temp of 18 degree . how much gas remains in the cylinder if the pressure is decreased to 650 psi at a temperature of 26 degree of 26 degree c
Will you please read this and rephrase it. "contains 1.00 WHAT into 1000 g argon gas"
To calculate the amount of gas remaining in the cylinder, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature in Kelvin
First, we need to convert the temperature from Celsius to Kelvin:
T = 18°C + 273.15 = 291.15 K (for the initial conditions)
T = 26°C + 273.15 = 299.15 K (for the final conditions)
Now, let's calculate the volume of the gas using the initial conditions.
Since we don't have the value for volume, we need to rearrange the ideal gas law equation to solve for V:
V = (nRT) / P
Rearranging the formula:
V = [(m/M)RT] / P
Where:
m = mass of the gas (given as 1.00 × 10^3 g)
M = molar mass of argon (39.95 g/mol)
R = ideal gas constant (0.0821 L·atm/(mol·K))
P = pressure (given as 2050 psi, which will be converted to atm)
First, convert the pressure from psi to atm:
1 atm = 14.7 psi
So, 2050 psi = 2050/14.7 = 139.5 atm
Now, let's calculate the volume using the initial conditions:
V_initial = [(m/M)RT] / P
= [(1000 g / 39.95 g/mol) x (0.0821 L·atm/(mol·K)) x 291.15 K] / 139.5 atm
After calculating the above equation, you will get the initial volume (V_initial).
Next, let's calculate the final volume (V_final) using the final conditions. We will use the same equation:
V_final = [(m/M)RT] / P
= [(1000 g / 39.95 g/mol) x (0.0821 L·atm/(mol·K)) x 299.15 K] / 650 atm
After calculating the above equation, you will get the final volume (V_final).
Finally, we can calculate the amount of gas remaining in the cylinder:
By using the equation of state of an ideal gas, we can say that the ratio of the initial to final amounts of gas is equal to the ratio of the initial to final volumes:
n_initial / n_final = V_initial / V_final
Since we know the initial amount of gas (1.00 × 10^3 g) and we want to find the final amount of gas (n_final), rearrange the equation:
n_final = (n_initial x V_final) / V_initial
Now you can substitute the calculated values of V_initial, V_final, and n_initial into the equation to find the remaining amount of gas in the cylinder (n_final).