200 ml of a gas at 27oC and 1140 Pa pressure is transferred to a vessel of 450 ml capacity. What temperature is to be applied, if the pressure applied is 2000 Pa?
The grade is not the subject.
Just remember that PV/T = nR = constant
T must be in Kelvin.
1140*200/300 = 2000*450/T2
Solve for T2 (in K). Then convert to degrees C.
To solve this problem, we can use the ideal gas law, which states:
PV = nRT
Where:
P = pressure (in Pa)
V = volume (in liters)
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature (in Kelvin)
Let's start by finding the number of moles of the gas in the first vessel.
Given:
Initial volume (V1) = 200 ml = 0.2 L
Initial pressure (P1) = 1140 Pa
Temperature (T1) = 27oC = 27 + 273 = 300 K
We can rearrange the ideal gas law to solve for n:
n = PV / RT
n1 = (P1 * V1) / (R * T1)
Next, we need to calculate the number of moles in the second vessel.
Volume of second vessel (V2) = 450 ml = 0.45 L
Pressure in second vessel (P2) = 2000 Pa
We can rearrange the ideal gas law to solve for T2 (the temperature in the second vessel):
T2 = (P2 * V2) / (n1 * R)
Now, let's substitute the known values into the equation:
T2 = (2000 * 0.45) / (n1 * 8.314)
We just need to calculate the value of n1 and substitute it into the equation to find the temperature.
n1 = (P1 * V1) / (R * T1)
= (1140 * 0.2) / (8.314 * 300)
≈ 0.009
T2 = (2000 * 0.45) / (0.009 * 8.314)
≈ 12291.198 K
Therefore, the temperature to be applied to the second vessel is approximately 12291.198 K.
To solve this problem, we can use the ideal gas law, which states that the product of pressure (P), volume (V), and temperature (T) is constant for a given amount of gas.
The equation for the ideal gas law is:
PV = nRT,
where P is the pressure, V is the volume, n is the number of moles of gas, R is the ideal gas constant, and T is the temperature in Kelvin.
To find the temperature in the new vessel, we need to use the initial conditions and then use the same equation to determine the new temperature.
Step 1: Convert the initial temperature from Celsius to Kelvin.
The initial temperature is given as 27°C. To convert it to Kelvin, we add 273.15.
T1 = 27°C + 273.15 = 300.15 K
Step 2: Calculate the initial number of moles.
We can assume that the gas is ideal and use the ideal gas law to find the initial number of moles.
PV = nRT
n1 = (PV1) / (RT1)
n1 = (1140 Pa * 0.2 L) / (8.314 J/mol·K * 300.15 K)
n1 ≈ 0.095 mol
Step 3: Determine the new temperature.
Using the ideal gas law, we can calculate the new temperature.
PV = nRT
T2 = (PV2) / (n2R)
T2 = (2000 Pa * 0.45 L) / (0.095 mol * 8.314 J/mol·K)
T2 ≈ 1052.68 K
Therefore, the temperature that should be applied to achieve a pressure of 2000 Pa in the vessel with a capacity of 450 ml is approximately 1052.68 Kelvin (K).