Question

A student doing this experiment collected the following data:

Temperature of boiling water: 99.7 C

Volume of water pulled into flask: 30.0 mL

Temperature of water in ice-water bath: 0.1 C

Volume of flask: 134.0 mL

barometric pressure: 28.5 in. Hg

1. Find the volume of wet, cold air

2. Convert the barometric pressure from in. Hg to torr.

3. Calculate the pressure of cold, dry air

4. Calculate the volume of dry, cold air

5. Convert the temperature of boiling-water and ice-water baths from Celsius to Kelvin

6. Find the volume-to-temperature ratio for the volume of the hot, dry air at the temperature of the boiling water bath

7. Find the volume-to-temperature ratio for the volume of cold, dry air at the temperature of the ice-water bath.

8. Briefly explain why these values do or do not verify Charles's Law

Answer 1

Given: Temprature of boiling water = 99.7⁰C (T₁)

volume of water pulled into flask = 30.0 mL

Temperature of water in ice-water bath = 0.1⁰C (T₂)

volume of flask = 134.0 mL

barometric pressure (atmospheric)= 28.5 in Hg

Hence, volume of hot dry air = total volume of flask = 134.0 mL (V₁)

1. Volume of wet, cold air = volume of flask - volume of water pulled in = 134.0 mL - 30.0 mL = 104.0 mL

2. Convert barometric pressure to torr

Use, 1 in Hg = 25.4 torr

Hence, 28.5 in Hg = 723.9 torr

3. Calculate the pressure of cold, dry air

Pressure of dry air = Atmospheric pressure - vapor pressure of water at T₂ = 723.9 torr - 5 torr = 718.9 torr

4. To calculate volume of dry gas at atmospheric pressure solve Boyle's law for the corrected volume

(P_drygas ) * (Volume at T₂) = (P_atm) * (V_corrected)

Thus, volume of dry gas(corrected) = (P_drygas ) * (Volume at T₂) / P_atm = (718.9 torr * 104.0 mL) / 723.9 torr = 103.3 mL

This is volume of dry cold air (V₂) .

5. Convert the temperatures T₁ and T₂ from celcius to kelvin

Use following relation:

Kelvin = ⁰C + 273

So, T₁ = 99.7 + 273 = 372.7 K

T₂ = 0.1 + 273 = 273.1 K

6. Now calculate the volume to temerature ratio for the volume of hot, dry air at the temperature of the boiling water bath.

V₁/T₁ = 134.0 mL / 372.7 K = 0.36

7. Calculate the volume to temerature ratio for thr volume of cold dry air at the temperature of the ice-water bath.

V₂/T₂ = 103.3 mL / 273.1 = 0.38

8. The near equality of the two ratios above(7) can be attributed to Charles law. Charles law relates the volume and temperature of a gas. As the temperature increases volume also increases.

Hence, if the charles law is obeyed, then

V₁/T₁ = V₂/T₂

Therefore in the given case as the V/T ratio for hot and cold air are very close, Charles law is verified.