a gas occupies 200ml volume at temperature of 20C. what volume does it occupy at a temperature of -40C.
(V1/T1) = (V2/T2)
T must be in kelvin.
To calculate the volume of the gas at a different temperature, we need to use Charles's Law, which states that the volume of a gas is directly proportional to its temperature, assuming pressure and amount of gas are held constant.
Charles's Law can be mathematically expressed as:
V1 / T1 = V2 / T2
Where:
V1 = Initial volume of the gas (200 mL)
T1 = Initial temperature in Kelvin (20 °C + 273.15 = 293.15 K)
V2 = Volume of the gas at a different temperature (unknown)
T2 = Temperature in Kelvin (-40 °C + 273.15 = 233.15 K)
Now, let's solve for V2 using the given values:
V1 / T1 = V2 / T2
200 mL / 293.15 K = V2 / 233.15 K
Cross-multiplying:
(200 mL) × (233.15 K) = (293.15 K) × V2
46,630 mL·K = 293.15 K × V2
Dividing both sides by 293.15 K:
46,630 mL·K / 293.15 K = V2
V2 ≈ 159.09 mL
Therefore, the volume of the gas at a temperature of -40 °C would be approximately 159.09 mL.