The total kinetic energy of 1 mole of oxygen at 27°C is :
[Use universal gas constant (R)= 8.31 J/mole K]
[Use universal gas constant (R)= 8.31 J/mole K]
- 6232.5 J
- 6845.5 J
- 5942.0 J
- 5670.5 J
The Correct Option is A
Approach Solution - 1
To determine the total kinetic energy of 1 mole of oxygen at 27°C, we can use the formula for the kinetic energy of gases as derived from the kinetic theory of gases. The kinetic energy of one mole of a diatomic gas like oxygen can be given by:
\[\text{Total Kinetic Energy} = \frac{5}{2} nRT\]
where:
- \(n\) is the number of moles, which is 1 mole in this case.
- \(R\) is the universal gas constant, given as 8.31 J/mole K.
- \(T\) is the absolute temperature in Kelvin.
First, convert the given temperature from Celsius to Kelvin:
T = 27 + 273.15 = 300.15 \text{ K}
For simplicity, we round off to 300 K. Substitute these values into the kinetic energy formula:
\[\text{Total Kinetic Energy} = \frac{5}{2} \times 1 \times 8.31 \times 300\]
Calculating this gives:
\[\text{Total Kinetic Energy} = \frac{5}{2} \times 8.31 \times 300 = 6232.5 \text{ J}\]
Thus, the total kinetic energy of 1 mole of oxygen at 27°C is 6232.5 J. This confirms that the correct answer is
6232.5 J
.
The other options are incorrect as they do not match the calculated value based on the kinetic theory of gases.
Approach Solution -2
The kinetic energy of a gas is given by:
\(E = \frac{f}{2} nRT,\)
where \(f\) is the degrees of freedom.
For a diatomic gas like oxygen:
- \(f = 5\),
- \(n = 1\),
- \(R = 8.31 \, \text{J/molK}\),
- \(T = 27^\circ \text{C} = 300 \, \text{K}\).
Substituting the values:
\(E = \frac{5}{2} \times 1 \times 8.31 \times 300 = 6232.5 \, \text{J}.\)
The correct option is (A) : 6232.5 J
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Concepts Used:
Kinetic energy
Kinetic energy of an object is the measure of the work it does as a result of its motion. Kinetic energy is the type of energy that an object or particle has as a result of its movement. When an object is subjected to a net force, it accelerates and gains kinetic energy as a result. Kinetic energy is a property of a moving object or particle defined by both its mass and its velocity. Any combination of motions is possible, including translation (moving along a route from one spot to another), rotation around an axis, vibration, and any combination of motions.
