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Question: A cylinder contains acetylene gas at \( {{27}^{o}}C \) and \( 4.05\text{ }MPa. \) The pressure in th...

A cylinder contains acetylene gas at 27oC{{27}^{o}}C and 4.05 MPa.4.05\text{ }MPa. The pressure in the cylinder after half the mass of gas is used up and temperature has fallen to 12oC{{12}^{o}}C will be:
(A) 4.05 Mpa4.05\text{ }Mpa
(B) 2.025 Mpa2.025\text{ }Mpa
(C) 3.84 Mpa3.84\text{ }Mpa
(D) 1.92 Mpa1.92\text{ }Mpa

Explanation

Solution

Hint : We know that the By using the ideal gas equation as: pV=nRTpV=nRT , we can find the value of the ideal gas constant by putting the values of pressure, volume, temperature and number of moles. Now solve it.

Complete Step By Step Answer:
We know that the ideal gas equation is: pV=nRTpV=nRT
Here p represents pressure of the gas in Pascal , V represents the volume of the gas in liters, n represents the no. of moles of the gas, R is the ideal gas constant or the universal gas constant and T is the temperature of the gas in kelvin.
The equation of the ideal gas i.e. is used in those conditions when either temperature, volume or pressure of a gas are constant or in those situations when out of the four properties i.e. pressure, volume, number of moles and temperature of the gas , three properties of a gas are given. Now considering the statement;
PV=wMwRT ˋPV=\dfrac{w}{Mw}RT\grave{\ }
Also we know that; PwT= constant\dfrac{P}{wT}=~constant .
PV=P1w1T1=P2w2T2PV=\dfrac{{{P}_{1}}}{{{w}_{1}}{{T}_{1}}}=\dfrac{{{P}_{2}}}{{{w}_{2}}{{T}_{2}}}
By putting all the given values, we get;
PV=4.05w×300=P2w2×285PV=\dfrac{4.05}{w\times 300}=\dfrac{{{P}_{2}}}{\dfrac{w}{2}\times 285}
Therefore, we get value of P2{{P}_{2}} ;
⇒P2=1.92MPa.\Rightarrow {{P}_{2}}=1.92MPa.
Therefore, the correct answer is option D.

Additional Information:
Molar volume: The volume occupied by one mole of substance at a given temperature and pressure is called molar volume. It is usually applied to the gases where the nature of the gas does not affect the volume. The most general example is that the molar volume of gas at standard temperature-pressure condition is equal to 22.4L22.4L for one mole of an ideal gas at temperature equal to 273K273K and pressure equal to 1atm.1atm.

Note :
Now we can see the difference between STP and NTP. Standard temperature and pressure condition is known as STP. The standard temperature value is and the standard pressure value is or Normal Temperature and Pressure is known as NTP the value of pressure at NTP is and the temperature at NTP.