Exciting Gas Volume Calculation with Charles's Law

How to determine the volume of a gas sample at different temperatures using Charles's Law?

Given data: A gas sample occupies 3.50 liters of volume at 20 degrees C. What volume will this gas occupy at 100 degrees C (reported to three significant figures)?

A) 0.224 L

B) 2.75 L

C) 4.46 L

D) 17.5 L

E) none of the above

Answer:

The gas sample will occupy a volume of 4.435 liters at 100 degrees C.

The relationship between volume and temperature of a gas can be described using Charles's Law. According to this law, at constant pressure, the volume of a gas is directly proportional to its temperature. This can be expressed mathematically as:

V1 / T1 = V2 / T2

Where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature. In this case, the initial volume is 3.50 liters at 20 degrees C, and the final temperature is 100 degrees C. Plugging in these values into the equation, we can solve for V2:

(3.50L / 293K) = (V2 / 373K)

V2 = (3.50L x 373K) / 293K = 4.435L

Thus, the gas sample will occupy a volume of approximately 4.435 liters at 100 degrees C.