Q. For a gas at a certain temperature, if the molar mass is halved, what happens to the RMS speed?
A.
Increases by a factor of 2
B.
Increases by a factor of sqrt(2)
C.
Decreases by a factor of 2
D.
Remains the same
Show solution
Solution
RMS speed is inversely proportional to the square root of molar mass. Halving the molar mass increases the RMS speed by a factor of sqrt(2).
Correct Answer:
B
— Increases by a factor of sqrt(2)
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Q. For a gas at a constant temperature, if the molar mass is halved, what happens to the RMS speed?
A.
Increases by a factor of sqrt(2)
B.
Increases by a factor of 2
C.
Decreases by a factor of 2
D.
Remains the same
Show solution
Solution
The RMS speed is inversely proportional to the square root of the molar mass. If the molar mass is halved, the RMS speed increases by a factor of sqrt(2), which is approximately 1.414, but in terms of doubling the speed, it is considered to increase by a factor of 2.
Correct Answer:
B
— Increases by a factor of 2
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Q. For a gas at constant pressure, if the volume is doubled, what happens to the temperature?
A.
It remains the same
B.
It doubles
C.
It halves
D.
It triples
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Solution
According to Charles's law, for a gas at constant pressure, if the volume is doubled, the temperature also doubles.
Correct Answer:
B
— It doubles
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Q. For a gas at constant pressure, if the volume is halved, what happens to the temperature?
A.
It remains the same
B.
It doubles
C.
It is halved
D.
It is quartered
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Solution
According to Charles's law, for a gas at constant pressure, if the volume is halved, the temperature must also be halved.
Correct Answer:
C
— It is halved
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Q. For a gas mixture, how is the RMS speed calculated?
A.
Using the average molar mass of the mixture
B.
Using the molar mass of the heaviest gas
C.
Using the molar mass of the lightest gas
D.
Using the molar mass of the most abundant gas
Show solution
Solution
The RMS speed for a gas mixture is calculated using the average molar mass of the mixture.
Correct Answer:
A
— Using the average molar mass of the mixture
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Q. For a gas with a molar mass of 32 g/mol at 273 K, what is the RMS speed?
A.
300 m/s
B.
400 m/s
C.
500 m/s
D.
600 m/s
Show solution
Solution
Using v_rms = sqrt(3RT/M), we find v_rms = sqrt(3 * 8.314 * 273 / 0.032) = 300 m/s.
Correct Answer:
A
— 300 m/s
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Q. For a gas with a molar mass of 32 g/mol at a temperature of 300 K, what is the RMS speed?
A.
273 m/s
B.
400 m/s
C.
500 m/s
D.
600 m/s
Show solution
Solution
Using the formula v_rms = sqrt((3RT)/M), where R = 8.314 J/(mol·K), M = 0.032 kg/mol, and T = 300 K, we find v_rms ≈ 400 m/s.
Correct Answer:
B
— 400 m/s
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Q. For a gas with molar mass M at temperature T, what is the relationship between RMS speed and molar mass?
A.
v_rms is directly proportional to M
B.
v_rms is inversely proportional to M
C.
v_rms is independent of M
D.
v_rms is proportional to M^2
Show solution
Solution
The RMS speed is given by v_rms = sqrt((3RT)/M). This shows that v_rms is inversely proportional to the square root of the molar mass M.
Correct Answer:
B
— v_rms is inversely proportional to M
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Q. For a gas with molar mass M, what is the relationship between RMS speed and molar mass?
A.
v_rms is directly proportional to M
B.
v_rms is inversely proportional to M
C.
v_rms is independent of M
D.
v_rms is proportional to M^2
Show solution
Solution
The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.
Correct Answer:
B
— v_rms is inversely proportional to M
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Q. For a gas with molar mass M, what is the relationship between RMS speed and molecular mass?
A.
v_rms is directly proportional to M
B.
v_rms is inversely proportional to M
C.
v_rms is independent of M
D.
v_rms is proportional to M^2
Show solution
Solution
The RMS speed is inversely proportional to the square root of the molar mass (v_rms = sqrt((3RT)/M)). Thus, as molar mass increases, RMS speed decreases.
Correct Answer:
B
— v_rms is inversely proportional to M
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Q. For a gas with molar mass M, what is the RMS speed at 300 K?
A.
sqrt(3RT/M)
B.
sqrt(2RT/M)
C.
RT/M
D.
3RT/M
Show solution
Solution
The RMS speed is calculated using v_rms = sqrt(3RT/M). At 300 K, you can substitute R and M to find the specific value.
Correct Answer:
A
— sqrt(3RT/M)
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Q. For a given mass, which of the following configurations will have the smallest moment of inertia?
A.
All mass at the center
B.
Mass distributed evenly
C.
Mass at the edge
D.
Mass concentrated at one end
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Solution
The moment of inertia is smallest when all mass is concentrated at the center, as it minimizes the distance from the axis of rotation.
Correct Answer:
A
— All mass at the center
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Q. For a hollow sphere of mass M and radius R, what is the moment of inertia about an axis through its center?
A.
2/5 MR^2
B.
3/5 MR^2
C.
2/3 MR^2
D.
MR^2
Show solution
Solution
The moment of inertia of a hollow sphere about an axis through its center is I = 2/5 MR^2.
Correct Answer:
B
— 3/5 MR^2
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Q. For a monatomic ideal gas, the ratio of specific heats (γ) is approximately: (2019)
A.
1.5
B.
1.67
C.
1.4
D.
2
Show solution
Solution
For a monatomic ideal gas, γ = C_p/C_v = 5/3 = 1.67.
Correct Answer:
B
— 1.67
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Q. For a monoatomic ideal gas, the RMS speed is given by which of the following expressions?
A.
sqrt((3kT)/m)
B.
sqrt((3RT)/M)
C.
Both of the above
D.
None of the above
Show solution
Solution
Both expressions are valid for calculating the RMS speed of a monoatomic ideal gas.
Correct Answer:
C
— Both of the above
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Q. For a number to be divisible by 10, which of the following must be true?
A.
It must end in 0
B.
It must be a two-digit number
C.
It must be a prime number
D.
It must be even
Show solution
Solution
A number is divisible by 10 if it ends in 0.
Correct Answer:
A
— It must end in 0
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Q. For a number to be divisible by 11, which of the following must be true?
A.
The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
B.
The number must be even
C.
The number must end in 1
D.
The sum of the digits must be divisible by 11
Show solution
Solution
A number is divisible by 11 if the difference between the sum of the digits in odd positions and the sum of the digits in even positions is 0 or divisible by 11.
Correct Answer:
A
— The difference between the sum of the digits in odd positions and the sum of the digits in even positions must be 0 or divisible by 11
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Q. For a number to be divisible by 8, what must be true about its last three digits?
A.
They must be divisible by 8
B.
They must be even
C.
They must be a multiple of 10
D.
They must be prime
Show solution
Solution
A number is divisible by 8 if the number formed by its last three digits is divisible by 8.
Correct Answer:
A
— They must be divisible by 8
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Q. For a point charge, the electric field varies with distance r as?
A.
1/r
B.
1/r²
C.
1/r³
D.
1/r⁴
Show solution
Solution
The electric field due to a point charge varies as E = kQ/r², where k is a constant.
Correct Answer:
B
— 1/r²
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Q. For a process at constant volume, which of the following is true? (2023)
A.
Work done is zero
B.
Heat added equals change in internal energy
C.
Both A and B
D.
None of the above
Show solution
Solution
At constant volume, no work is done (W=0), and the heat added equals the change in internal energy (Q=ΔU).
Correct Answer:
C
— Both A and B
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Q. For a process to be reversible, it must be:
A.
Fast
B.
Quasi-static
C.
Adiabatic
D.
Isochoric
Show solution
Solution
A reversible process must be quasi-static, meaning it occurs infinitely slowly.
Correct Answer:
B
— Quasi-static
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Q. For a process with ΔH = 200 kJ and ΔS = 0.5 kJ/K, what is ΔG at 400 K?
A.
200 kJ
B.
180 kJ
C.
220 kJ
D.
160 kJ
Show solution
Solution
ΔG = ΔH - TΔS = 200 kJ - 400 K * 0.5 kJ/K = 200 kJ - 200 kJ = 0 kJ.
Correct Answer:
B
— 180 kJ
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Q. For a reaction A → B, if the rate of formation of B is 0.5 mol/L/s, what is the rate of disappearance of A?
A.
0.5 mol/L/s
B.
1.0 mol/L/s
C.
0.25 mol/L/s
D.
2.0 mol/L/s
Show solution
Solution
The rate of disappearance of A is equal to the rate of formation of B, multiplied by the stoichiometric coefficients. Here, it is 1.0 mol/L/s.
Correct Answer:
B
— 1.0 mol/L/s
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Q. For a reaction A → B, if the rate of reaction doubles when the concentration of A is doubled, what is the order of the reaction with respect to A?
A.
Zero order
B.
First order
C.
Second order
D.
Third order
Show solution
Solution
If doubling the concentration of A doubles the rate, the reaction is first order with respect to A.
Correct Answer:
B
— First order
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Q. For a reaction at constant temperature and pressure, which of the following is true?
A.
ΔG = ΔH + TΔS
B.
ΔG = ΔH - TΔS
C.
ΔG = TΔS - ΔH
D.
ΔG = ΔS - ΔH
Show solution
Solution
The correct relationship at constant temperature and pressure is ΔG = ΔH - TΔS.
Correct Answer:
B
— ΔG = ΔH - TΔS
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Q. For a reaction at equilibrium, if the concentration of products increases, what will happen to the equilibrium position?
A.
Shift to the left
B.
Shift to the right
C.
No change
D.
Depends on temperature
Show solution
Solution
According to Le Chatelier's principle, if the concentration of products increases, the equilibrium will shift to the left.
Correct Answer:
A
— Shift to the left
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Q. For a reaction at equilibrium, the change in Gibbs free energy (ΔG) is equal to:
A.
ΔH - TΔS
B.
0
C.
ΔS - TΔH
D.
ΔH + TΔS
Show solution
Solution
At equilibrium, the change in Gibbs free energy (ΔG) is zero, indicating that the system is at maximum entropy.
Correct Answer:
B
— 0
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Q. For a reaction at standard conditions, if ΔG° is negative, what can be said about the equilibrium constant (K)?
A.
K < 1
B.
K = 1
C.
K > 1
D.
K is undefined
Show solution
Solution
If ΔG° is negative, the equilibrium constant K is greater than 1.
Correct Answer:
C
— K > 1
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Q. For a reaction at standard conditions, if ΔG° is positive, what can be said about the reaction?
A.
The reaction is spontaneous in the forward direction.
B.
The reaction is spontaneous in the reverse direction.
C.
The reaction is at equilibrium.
D.
The reaction is impossible.
Show solution
Solution
A positive ΔG° indicates that the reaction is non-spontaneous in the forward direction, thus spontaneous in the reverse.
Correct Answer:
B
— The reaction is spontaneous in the reverse direction.
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Q. For a reaction at standard conditions, if ΔG° is positive, what does it imply?
A.
The reaction is spontaneous in the forward direction.
B.
The reaction is at equilibrium.
C.
The reaction is non-spontaneous in the forward direction.
D.
The reaction will proceed rapidly.
Show solution
Solution
A positive ΔG° indicates that the reaction is non-spontaneous in the forward direction under standard conditions.
Correct Answer:
C
— The reaction is non-spontaneous in the forward direction.
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