Questions & Answers
Question
AnswersThe density of \[{{O}_{2}}\] is maximum at:
A. STP
B. 273K and 2atm
C. 546K and 1atm
D. 546K and 2atm
Answer
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Hint: We can solve this question by considering the ideal of ideal gas and correlating it with the density which is the ratio of mass to volume. The ideal gas equation is given as follows
\[PV=nRT\]
Where, n is the number of moles of the given gas, P is the pressure exerted by the gas, V is the volume occupied by the gas, T is the temperature of the gas and R is the universal gas constant.
Complete answer:
The ideal gas equation is given as follows,
\[PV=nRT\]
Now, we know that moles of a gas can be given as,
\[n=\dfrac{w}{M}\]
Where, n is the number of moles of the given compound, w is the weight of the given compound and M is the molar mass of the compound. Substituting the given value in the ideal gas equation we get,
\[PV=\dfrac{w}{M}RT\]
Now , we know Density, \[\rho =\dfrac{w}{V}\]
\[\rho =\dfrac{w}{V}=\dfrac{PM}{RT}\]
Thus we get the equation of the density of the ideal gas which says that the density is directly proportional to the pressure and inversely proportional to the temperature of the gas. Therefore, to achieve maximum density we must have maximum value of pressure and lower value of temperature.
Hence, option B is the correct option as it correctly represents the conditions for maximum density which is higher pressure and lower temperature. The correct answer is 273K and 2atm.
So, the correct answer is “Option B”.
Note:
STP is an abbreviation that stands for Standard Temperature and Pressure. At standard temperature and pressure, a system is said to have a temperature of zero degrees centigrade that is 273 Kelvins and the pressure of 1 atmosphere. Also, one mole of any gas at STP occupies a standard volume of 22.414 L.
\[PV=nRT\]
Where, n is the number of moles of the given gas, P is the pressure exerted by the gas, V is the volume occupied by the gas, T is the temperature of the gas and R is the universal gas constant.
Complete answer:
The ideal gas equation is given as follows,
\[PV=nRT\]
Now, we know that moles of a gas can be given as,
\[n=\dfrac{w}{M}\]
Where, n is the number of moles of the given compound, w is the weight of the given compound and M is the molar mass of the compound. Substituting the given value in the ideal gas equation we get,
\[PV=\dfrac{w}{M}RT\]
Now , we know Density, \[\rho =\dfrac{w}{V}\]
\[\rho =\dfrac{w}{V}=\dfrac{PM}{RT}\]
Thus we get the equation of the density of the ideal gas which says that the density is directly proportional to the pressure and inversely proportional to the temperature of the gas. Therefore, to achieve maximum density we must have maximum value of pressure and lower value of temperature.
Hence, option B is the correct option as it correctly represents the conditions for maximum density which is higher pressure and lower temperature. The correct answer is 273K and 2atm.
So, the correct answer is “Option B”.
Note:
STP is an abbreviation that stands for Standard Temperature and Pressure. At standard temperature and pressure, a system is said to have a temperature of zero degrees centigrade that is 273 Kelvins and the pressure of 1 atmosphere. Also, one mole of any gas at STP occupies a standard volume of 22.414 L.