the absolute temperature of the gas at which 3.33 10-3 mol occupies 246 mL at 713 torr
PV = nRT
To find the absolute temperature of the gas, we 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 = absolute temperature in Kelvin
First, let's convert the given values to appropriate units:
- The volume is given as 246 mL, so we need to convert it to liters by dividing by 1000:
V = 246 mL / 1000 mL/L = 0.246 L
- The number of moles is given as 3.33 x 10^(-3) mol.
- The pressure is given as 713 torr. Since the ideal gas law requires pressure in atm, we need to convert it by dividing by 760 torr/atm:
P = 713 torr / 760 torr/atm ≈ 0.937 atm
Now, let's substitute the values into the ideal gas law equation:
(0.937 atm)(0.246 L) = (3.33 x 10^(-3) mol)(0.0821 L.atm/mol.K)(T)
Simplifying the equation:
0.230 L.atm = 2.73 x 10^(-4) L.atm/mol.K (T)
Now, divide both sides of the equation by 2.73 x 10^(-4) L.atm/mol.K to isolate T:
T = (0.230 L.atm) / (2.73 x 10^(-4) L.atm/mol.K)
Calculating T:
T = 842.67 K
Therefore, the absolute temperature of the gas is approximately 842.67 K.