Calculate the volume at s.t.p. occupied by a dry gas 'Q' originally occupying 153.7cc at 287K and 750mm pressure [vapor pressure
of gas 'Q'at 287K is 12mm of Hg]
See your other post above.
To calculate the volume of the gas at standard temperature and pressure (STP), we will use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (0.0821 L atm/mol K)
T = temperature in Kelvin
Given data:
Initial volume (V_initial) = 153.7 cc = 153.7 mL = 0.1537 L
Initial temperature (T_initial) = 287 K
Initial pressure (P_initial) = 750 mmHg
Vapor pressure of gas Q at T_initial = 12 mmHg
First, let's convert the pressures to atmospheres (atm) since the ideal gas constant is usually given in terms of atm.
P_initial = 750 mmHg / 760 mmHg/atm = 0.9868 atm
Vapor pressure (P_vapor) = 12 mmHg / 760 mmHg/atm = 0.0158 atm
Next, to calculate the number of moles (n), we can use the ideal gas law equation rearranged to solve for moles:
n = PV / RT
Let's calculate the number of moles of gas Q:
n = (P_initial - P_vapor) * V_initial / (R * T_initial)
= (0.9868 atm - 0.0158 atm) * 0.1537 L / (0.0821 L atm/mol K * 287 K)
≈ 0.0261 moles
Now, we can use the ideal gas law equation to find the final volume (V_final) at STP:
P_final = 1 atm (since STP is defined as 1 atm)
T_final = 273.15 K (standard temperature at STP)
V_final = nRT_final / P_final
= 0.0261 moles * 0.0821 L atm/mol K * 273.15 K / 1 atm
≈ 0.591 L or 591 cc
Therefore, the volume occupied by the dry gas Q at STP is approximately 591 cc.