A tank contains 10.5 g of chlorine gas (Cl2) at a temperature of 87 °C and an absolute pressure of 5.50 × 105 Pa. The mass per mole of Cl2 is 70.9 g/mol.
(a) Determine the volume of the tank.
(b) Later, the temperature of the tank has dropped to 30 °C and, due to a leak, the pressure has dropped to 3.70 × 105 Pa. How many grams of chlorine gas have leaked out of the tank?
To solve these problems, we can 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 in Kelvin.
First, let's convert the temperature from Celsius to Kelvin.
(a) Convert 87 °C to Kelvin:
T = 87 °C + 273.15 = 360.15 K
Now, let's solve for the volume of the tank.
We have:
Mass of chlorine gas (Cl2) = 10.5 g
Mass per mole of Cl2 = 70.9 g/mol
Number of moles (n) = mass / molar mass = 10.5 g / 70.9 g/mol ≈ 0.148 moles
The ideal gas constant (R) is 8.314 J/(mol·K).
Now, we can rearrange the ideal gas law equation to solve for V:
V = (nRT) / P
Substituting the given values, we get:
V = (0.148 mol * 8.314 J/(mol·K) * 360.15 K) / (5.50 × 10^5 Pa)
Calculating this expression will give us the volume of the tank.
(b) For the second part of the question, we need to find the grams of chlorine gas leaked out.
Convert 30 °C to Kelvin:
T = 30 °C + 273.15 = 303.15 K
Given:
Pressure (P) = 3.70 × 10^5 Pa
Using the ideal gas law equation, we can solve for the number of moles (n2) using the new conditions:
n2 = (PV) / (RT)
Substituting the given values:
n2 = (3.70 × 10^5 Pa * V) / (8.314 J/(mol·K) * 303.15 K)
Since the initial number of moles (n1) was 0.148 moles (as calculated in part a), we can find the moles leaked (nleaked) as:
nleaked = n1 - n2
Finally, we can calculate the grams of chlorine gas that leaked out by multiplying the number of moles leaked by the molar mass:
Mass leaked (in grams) = nleaked * molar mass of Cl2.
P V = n R T
p in Pascals
n in mols
T in kelvin (C+273)
v in cm^3
----> R = 8.31*10^6 http://www.katmarsoftware.com/gconvals.htm
here
n = 10.5/70.9
T = 273+87
P = 5.5 * 10^5
R = 8.31*10^6