300 ml of a gas at 27oC is cooled to 3oC at constant pressure.its final volume is? [please explain clearly]
You know that PV=kT
Since P is held constant, that means that
V/T = k/P, which is constant.
The temperature is reduced by a factor of (273+3)/(273+27), so the volume must also decrease by the same factor for V/T to remain constant.
To find the final volume of the gas when it is cooled from 27°C to 3°C at constant pressure, we can use the ideal gas law. The ideal gas law equation is given by:
PV = nRT
Where:
P = pressure (constant in this case)
V = volume
n = number of moles of gas
R = ideal gas constant
T = temperature in Kelvin
First, let's convert the temperatures from degrees Celsius to Kelvin. We add 273 to each temperature:
Initial temperature (T1) = 27°C + 273 = 300 K
Final temperature (T2) = 3°C + 273 = 276 K
Since the pressure (P) is constant, we can rewrite the ideal gas law equation as:
V1/T1 = V2/T2
Now, we can rearrange the equation to solve for V2:
V2 = (V1 * T2) / T1
Given:
V1 = 300 ml = 300 cm³
T1 = 300 K
T2 = 276 K
Substituting the values into the equation:
V2 = (300 cm³ * 276 K) / 300 K
Simplifying:
V2 = (300 cm³ * 276) / 300
V2 = 27600 / 300
V2 = 92 cm³
Therefore, the final volume of the gas is 92 cm³.