a 100 cm cube gas cylinder filled with chlorine under 160 torr pressure is connected by stop clock with another cylinder of 400 cm cube filled with nitrogen under pressure of200 torr. what will be total pressure when stop clock is opened?
To find the total pressure when the stop clock is opened, we need to use the combined gas law:
(P1 * V1) / T1 = (P2 * V2) / T2
Where:
P1 = initial pressure of the chlorine gas cylinder = 160 torr
V1 = initial volume of the chlorine gas cylinder = 100 cm^3
T1 = initial temperature of the chlorine gas cylinder (assuming constant)
P2 = initial pressure of the nitrogen gas cylinder = 200 torr
V2 = initial volume of the nitrogen gas cylinder = 400 cm^3
T2 = initial temperature of the nitrogen gas cylinder (assuming constant)
Since the gases are connected by a stop clock, their temperatures and volumes remain constant. Thus, we can simplify the equation to:
P1 / P2 = V1 / V2
Let's substitute the given values:
P1 = 160 torr
V1 = 100 cm^3
P2 = 200 torr
V2 = 400 cm^3
Now, we can solve for the total pressure by rearranging the equation:
Total Pressure = (P1 * V1) / V2
Total Pressure = (160 torr * 100 cm^3) / 400 cm^3
Total Pressure = 40 torr
Therefore, the total pressure when the stop clock is opened will be 40 torr.
To calculate the total pressure when the stop clock is opened, we need to consider the ideal gas law. The ideal gas law states that the pressure of a gas is directly proportional to the number of gas molecules and the temperature, and inversely proportional to the volume of the container.
In this case, we have two cylinders connected by a stop clock. Let's calculate the number of moles of chlorine gas in the first cylinder and the number of moles of nitrogen gas in the second cylinder.
To calculate the number of moles of a gas, we can use the formula:
n = PV / RT
Where:
n = number of moles
P = pressure in atmospheres (we need to convert from torr to atm by dividing by 760)
V = volume in liters (we need to convert from cm³ to liters by dividing by 1000)
R = ideal gas constant (0.0821 L·atm/(mol·K))
T = temperature in Kelvin
For the chlorine gas cylinder:
P₁ = 160 torr / 760 = 0.211 atm
V₁ = 100 cm³ / 1000 = 0.1 L
For the nitrogen gas cylinder:
P₂ = 200 torr / 760 = 0.263 atm
V₂ = 400 cm³ / 1000 = 0.4 L
Assuming both cylinders are at the same temperature, we can use the ideal gas law to calculate the number of moles:
n₁ = (0.211 atm * 0.1 L) / (0.0821 L·atm/(mol·K) * T)
n₂ = (0.263 atm * 0.4 L) / (0.0821 L·atm/(mol·K) * T)
Now, since the stop clock is opened, the two cylinders will mix together. The total number of moles of gas will be the sum of the moles of chlorine and nitrogen gas:
n_total = n₁ + n₂
Finally, to get the total pressure in the combined cylinder, we can use the ideal gas law again:
P_total = (n_total * R * T) / (V₁ + V₂)
Keep in mind that you'll need to know the temperature in Kelvin to calculate the final answer.