Oxygen gas having a volume of 784 cm3 at 23.3°C and 1.03 x 105 Pa expands until its volume is 1170 cm3 and its pressure is 1.07 x 105 Pa. Find (a) the number of moles of oxygen present and (b) the final temperature of the sample. (Unit kelvin, K, for part (b).)
Use the perfect gas law to get the number of moles, n. You can use initial condition values of p, V and T . The inital T is 296.5 K, V is 0.784 l and p = 1.017 atm. R = 0.08205 l-atm/mole
n = PV/RT = 0.0328 moles
The temperature after expansion depends upon the type of expansion. Usually an isentropic expansion is assumed, with the gas doing work while it pushes against an external boundary or gas. If it expands into a larger volume that had been previously empty, the gas temperature will not change.
For an isentropic expansion of a diatomic gas,
T^(5/2) * V = constant
The 5/2 exponent equals 1/[gamma - 1].
gamma = 1.4 for diatomics
(T'/296.5)^2.5 = 784/1170 = 0.670
T'/296.5 = 0.852
t' = 252.6 K = -20.6 C
thank u so much for the help
T' is supposed to be the final temperature
To solve this problem, we can use the ideal gas law equation:
PV = nRT
where:
P is the pressure of the gas
V is the volume of the gas
n is the number of moles of gas
R is the ideal gas constant (8.31 J/mol·K)
T is the temperature of the gas in Kelvin
Let's begin by finding the number of moles of oxygen using the initial conditions.
(a) Finding the number of moles of oxygen:
Given:
Initial volume (V1) = 784 cm3
Initial pressure (P1) = 1.03 x 105 Pa
Temperature (T1) = 23.3°C = 23.3 + 273.15 = 296.45 K (converting to Kelvin)
Using the ideal gas law equation, we have:
P1 * V1 = n * R * T1
Rearranging the equation to solve for n:
n = (P1 * V1) / (R * T1)
Substituting the given values, we have:
n = (1.03 x 105 Pa * 784 cm3) / (8.31 J/mol·K * 296.45 K)
Note: Before we can proceed with the calculation, we need to convert the initial volume from cm3 to m3, as the SI units should be used consistently. 1 cm3 = 1 x 10^-6 m3.
V1 = 784 cm3 * 1 x 10^-6 m3/cm3 = 7.84 x 10^-4 m3
Now we can calculate n:
n = (1.03 x 105 Pa * 7.84 x 10^-4 m3) / (8.31 J/mol·K * 296.45 K)
Calculating this expression gives us the number of moles of oxygen present.
(b) Finding the final temperature of the sample:
Given:
Final volume (V2) = 1170 cm3
Final pressure (P2) = 1.07 x 105 Pa
Using the ideal gas law equation again, we have:
P2 * V2 = n * R * T2
Solving for T2:
T2 = (P2 * V2) / (n * R)
Substituting the known values, we have:
T2 = (1.07 x 105 Pa * 1170 cm3) / (n * 8.31 J/mol·K)
Since we already calculated n in part (a), we can substitute its value into the equation and calculate T2.
Therefore, following these steps will enable us to find both the number of moles of oxygen present (part a) and the final temperature of the sample (part b).