A certain mass of a gas has a volume of 100 cc at 273° C and 700 mm Hg. What will be it's volume at S.T.P.
Chapter – Gas Laws
Sub – Chemistry
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Answers
STP is usually given as 273.15 K (0°C) and 1 atm.
The combined gas law can be used to answer this question. The formula is:
P1·V1/T1 = P2·V2/T2, where;
P1 = initial pressure = 1 atm
V1 = 27.3 cm^3
T1 = initial temperature 273.15 K
P2 = final pressure = ?
V2 = final temperature = 27.3 cm^3
T2 = 27°C + 273.15 = 300 K = 3.0×10^2 K to represent two significant figures
Rearrange the formula to isolate P2. Insert the known values and solve.
P2 = (P1·V1·T2)/(V2·T1)
P2 = (1 atm·27.3 cm^3·3.0×10^2 K)/(27.3 cm^3·273.15 K) = 1.1 atm to two significant figures
The pressure required is 1.1 atm.
Explanation:
Correct question:
- A certain mass of a gas has volume of 100 cm³ at 273°C. To what temperature must the gas be heated to make its final volume as 700 cm³. Assume that the pressure of the gas remains same.
Given:
- Initial volume (V₁) = 100 cm³
- Initial temperature (T₁) = 273°C
- Final volume (V₂) = 700 cm³
To find:
- Final temperature (T₂)
Solution:
Using Charles law:
=> V₁/T₁ = V₂/T₂
=> 100/273 = 700/T₂
=> T₂ = 700 × 273/100
=> T₂ = 1911°C
∴ The final temperature of the gas is 1911°C.
Verification:
=> V₁/T₁ = V₂/T₂
=> 100/273 = 700/1911
=> 0.36 = 0.36
∴ L.H.S = R.H.S
Learn more:
- Boyle's law: ''Temperature remaining constant- the volume of a given mass of dry gas is inversely proportional to its pressure.
=> V ∝ 1/P [ T = Constant]
=> PV = K
=> P₁V₁ = P₂V₂
- Charles' law: ''Pressure remaining constant- the volume of a given mass of dry gas is directly proportional to its absolute (Kelvin) temperature.
=> V ∝ T P = Constant]
∵ A certain mass of a gas has volume of 100 cm³ at 273°C. To what temperature must the gas be heated to make its final volume as 700 cm³. Assume that the pressure of the gas remains same is the right question.