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.