A 101 mL flask contains argon at 1.4 atm and
85◦C. What amount of Ar is present?
Answer in units of mol.
To calculate the amount of argon gas present in the flask, we can use the ideal gas law:
PV = nRT
Where:
P is the pressure of the gas,
V is the volume of the gas,
n is the number of moles,
R is the ideal gas constant (0.0821 L·atm/(mol·K)),
T is the temperature in Kelvin.
First, let's convert the temperature from Celsius to Kelvin:
T(Kelvin) = T(Celsius) + 273.15
T(Kelvin) = 85 + 273.15 = 358.15 K
Now we can rearrange the ideal gas law equation to solve for the number of moles (n):
n = (PV) / (RT)
n = (1.4 atm) * (101 mL) / (0.0821 L·atm/(mol·K) * 358.15 K)
To cancel out the units, we need to convert the mL to L:
1 mL = 0.001 L
n = (1.4 atm) * (0.101 L) / (0.0821 L·atm/(mol·K) * 358.15 K)
Now we can solve this expression to find the number of moles of argon gas present in the flask.
To find the amount of argon (Ar) present in the flask, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure (in atm)
V = volume (in liters)
n = number of moles of gas
R = ideal gas constant (0.0821 L·atm/mol·K)
T = temperature (in Kelvin)
To solve for n, we need to convert the given temperature from Celsius (°C) to Kelvin (K):
T(K) = T(°C) + 273.15
T(K) = 85 + 273.15 = 358.15 K
Now we can rearrange the ideal gas law equation to solve for n:
n = PV / RT
n = (1.4 atm) * (0.101 L) / (0.0821 L·atm/mol·K) * (358.15 K)
Now we can calculate the amount of Ar (in moles):
n = (1.4 * 0.101) / (0.0821 * 358.15)
n ≈ 0.00525 mol
Therefore, there is approximately 0.00525 moles of Ar present in the flask.