Question

What celsius temperature, rounded to the tenth of a degree, is required to change the volume of a gas sample (t = 8.9 ºc , v= 2.22×103 l ) to a volume of 2.52×103 l ?

Answer 1

To find the Celsius temperature required to change the volume of the gas sample, we can use Charles's law. Given the initial volume (V1 = 2.22×10^3 L) and temperature (T1 = 8.9 ºC) of the gas, and the desired volume (V2 = 2.52×10^3 L), we can solve for the unknown temperature (T2). Using the formula V1/T1 = V2/T2 and converting the temperatures to Kelvin, we find that the Celsius temperature required is approximately -262.4 ºC.

Step-by-step explanation:

To find the Celsius temperature required to change the volume of the gas sample, we can use Charles's law. Charles's law states that the volume of a gas is directly proportional to its temperature when pressure and amount of gas are kept constant. We are given the initial volume (V1 = 2.22×10^3 L) and temperature (T1 = 8.9 ºC) of the gas, and we want to find the temperature (T2) at which the volume (V2) is 2.52×10^3 L.

Using the formula V1/T1 = V2/T2 and converting the Celsius temperatures to Kelvin, we can set up the following equation:

(2.22×10^3 L)/(8.9 ºC + 273.15) = (2.52×10^3 L)/(T2 + 273.15)

Simplifying the equation, we can solve for T2:

233.61 = (2.52×10^3 L)/(T2 + 273.15)

Multiplying both sides of the equation by (T2 + 273.15), we get:

233.61(T2 + 273.15) = 2.52×10^3 L

Dividing both sides of the equation by 233.61, we get:

T2 + 273.15 = 10.79

Subtracting 273.15 from both sides of the equation, we find that:

T2 = -262.36

Rounding to the nearest tenth, the Celsius temperature required to change the volume of the gas sample to 2.52×10^3 L is -262.4 ºC.