What is the final volume (L) of a 1.00 L system at 315 K and 1.10 atm if STP conditions are established?
To find the final volume of the system at STP conditions, we need to 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.
First, let's calculate the initial number of moles (n1) of the system. Since we don't have the moles, we can use the ideal gas law to find it. Rearranging the formula, we get:
n1 = PV / RT
Substituting the given values:
P = 1.10 atm,
V = 1.00 L,
R = 0.0821 L·atm/(K·mol), and
T = 315 K,
n1 = (1.10 atm * 1.00 L) / (0.0821 L·atm/(K·mol) * 315 K)
n1 = 0.0427 mol
Now that we have the initial number of moles, let's calculate the final volume (V2) at STP conditions. At STP, the temperature (T2) is 273.15 K and the pressure (P2) is 1.00 atm.
Using the ideal gas law equation again:
P2 * V2 = n1 * R * T2
Substituting the given values:
P2 = 1.00 atm,
n1 = 0.0427 mol,
R = 0.0821 L·atm/(K·mol), and
T2 = 273.15 K,
(1.00 atm * V2) = (0.0427 mol * 0.0821 L·atm/(K·mol) * 273.15 K)
V2 = (0.0427 mol * 0.0821 L·atm/(K·mol) * 273.15 K) / (1.00 atm)
V2 = 0.945 L
Therefore, the final volume (V2) of the system at STP conditions would be 0.945 L.