Q. What is the pH of a 0.1 M solution of sodium bicarbonate (NaHCO3)?
-
A.
7.5
-
B.
8.4
-
C.
9.0
-
D.
6.0
Solution
NaHCO3 is a weak base; its pH is around 8.4.
Correct Answer: B — 8.4
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Q. What is the pH of a buffer solution containing 0.1 M acetic acid and 0.1 M sodium acetate?
-
A.
4.74
-
B.
5.74
-
C.
6.74
-
D.
7.74
Solution
Using the Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]). Here, pKa ≈ 4.74, so pH = 4.74 + log(1) = 4.74.
Correct Answer: A — 4.74
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Q. What is the pH of a buffer solution containing 0.2 M acetic acid and 0.1 M sodium acetate?
-
A.
4.76
-
B.
5.00
-
C.
5.74
-
D.
6.00
Solution
Using the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]) = 4.76 + log(0.1/0.2) = 5.74
Correct Answer: C — 5.74
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Q. What is the pH of a buffer solution made from 0.2 M acetic acid and 0.2 M sodium acetate?
-
A.
4.76
-
B.
5.76
-
C.
6.76
-
D.
7.76
Solution
Using the Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]) = 4.76.
Correct Answer: A — 4.76
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Q. What is the pH of a neutral solution at 25°C?
Solution
At 25°C, the pH of a neutral solution is 7.
Correct Answer: B — 7
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Q. What is the pH of a neutral solution of hydrogen ions?
Solution
A neutral solution has a pH of 7.
Correct Answer: B — 7
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Q. What is the pH of a solution formed by mixing equal volumes of 0.1 M HCl and 0.1 M NaOH?
Solution
HCl and NaOH neutralize each other completely, resulting in a neutral solution with a pH of 7.
Correct Answer: A — 7
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Q. What is the pH of a solution that has a hydrogen ion concentration of 1 x 10^-5 M?
Solution
pH is calculated as pH = -log[H+]. For [H+] = 1 x 10^-5 M, pH = -log(1 x 10^-5) = 5.
Correct Answer: A — 5
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Q. What is the pH of a solution that has a hydronium ion concentration of 1 x 10^-5 M?
Solution
pH is calculated as pH = -log[H3O+]. For [H3O+] = 1 x 10^-5 M, pH = -log(1 x 10^-5) = 5.
Correct Answer: A — 5
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Q. What is the pH of a solution that has a hydroxide ion concentration of 1.0 x 10^-3 M?
Solution
pOH = -log[OH-] = -log(1.0 x 10^-3) = 3. Therefore, pH = 14 - pOH = 14 - 3 = 11.
Correct Answer: A — 11
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Q. What is the pH of a solution that has a [H+] concentration of 1 x 10^-7 M?
Solution
pH = -log[H+] = -log(1 x 10^-7) = 7.
Correct Answer: A — 7
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Q. What is the pH of a solution that is 0.1 M in both acetic acid and sodium acetate?
-
A.
4.76
-
B.
5.76
-
C.
6.76
-
D.
7.76
Solution
Using Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]); pKa of acetic acid = 4.76, so pH = 4.76 + log(1) = 4.76
Correct Answer: A — 4.76
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Q. What is the pH of a solution with a hydroxide ion concentration of 0.001 M?
Solution
pOH = -log[OH-] = -log(0.001) = 3; pH = 14 - pOH = 14 - 3 = 11
Correct Answer: B — 12
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Q. What is the pH of a solution with a hydroxide ion concentration of 1.0 x 10^-4 M?
Solution
To find the pH, first calculate pOH = -log[OH-] = 4, then use pH + pOH = 14, so pH = 14 - 4 = 10.
Correct Answer: A — 10
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Q. What is the pH of a solution with [H+] = 1 x 10^-6 M?
Solution
Using the formula pH = -log[H+], we find pH = -log(1 x 10^-6) = 6.
Correct Answer: A — 6
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Q. What is the phase difference between the displacement and acceleration in simple harmonic motion?
-
A.
0 degrees
-
B.
90 degrees
-
C.
180 degrees
-
D.
270 degrees
Solution
In simple harmonic motion, acceleration is always opposite to displacement, hence the phase difference is 180 degrees.
Correct Answer: C — 180 degrees
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Q. What is the phase difference between the displacement and acceleration of a particle in simple harmonic motion?
-
A.
0 degrees
-
B.
90 degrees
-
C.
180 degrees
-
D.
270 degrees
Solution
In simple harmonic motion, the acceleration is always directed towards the mean position and is 180 degrees out of phase with the displacement.
Correct Answer: C — 180 degrees
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Q. What is the phase difference between the displacement and acceleration of a simple harmonic oscillator?
-
A.
0 degrees
-
B.
90 degrees
-
C.
180 degrees
-
D.
270 degrees
Solution
In simple harmonic motion, acceleration is 180 degrees out of phase with displacement.
Correct Answer: C — 180 degrees
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Q. What is the phase difference between the driving force and the displacement in a damped forced oscillator at resonance?
-
A.
0°
-
B.
90°
-
C.
180°
-
D.
270°
Solution
At resonance, the phase difference is 90°.
Correct Answer: B — 90°
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Q. What is the phase difference between the driving force and the displacement in a damped oscillator at resonance?
-
A.
0 degrees
-
B.
90 degrees
-
C.
180 degrees
-
D.
270 degrees
Solution
At resonance, the phase difference between the driving force and the displacement is 180 degrees.
Correct Answer: C — 180 degrees
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Q. What is the phase difference between the driving force and the displacement in a forced oscillation at resonance?
-
A.
0 degrees
-
B.
90 degrees
-
C.
180 degrees
-
D.
270 degrees
Solution
At resonance, the phase difference between the driving force and the displacement is 0 degrees.
Correct Answer: A — 0 degrees
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Q. What is the phase difference between two particles in simple harmonic motion that are in the same position at the same time?
Solution
If two particles are in the same position at the same time in simple harmonic motion, they have a phase difference of 0.
Correct Answer: A — 0
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Q. What is the phase difference between two particles in simple harmonic motion that are in phase?
-
A.
0 radians
-
B.
π/2 radians
-
C.
π radians
-
D.
3π/2 radians
Solution
When two particles are in phase, they reach their maximum and minimum displacements at the same time, resulting in a phase difference of 0 radians.
Correct Answer: A — 0 radians
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Q. What is the phase difference between two particles in simple harmonic motion that are 90 degrees out of phase?
-
A.
0 radians
-
B.
π/2 radians
-
C.
π radians
-
D.
3π/2 radians
Solution
A phase difference of 90 degrees corresponds to π/2 radians.
Correct Answer: B — π/2 radians
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Q. What is the phase difference between two particles in the same wave at a distance of λ/2?
-
A.
0 radians
-
B.
π/2 radians
-
C.
π radians
-
D.
3π/2 radians
Solution
The phase difference between two points in the same wave separated by a distance of λ/2 is π radians.
Correct Answer: C — π radians
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Q. What is the phase difference between two points on a wave that are 1/4 wavelength apart?
-
A.
0 radians
-
B.
π/2 radians
-
C.
π radians
-
D.
3π/2 radians
Solution
The phase difference Δφ between two points separated by a distance of λ/4 is given by Δφ = (2π/λ)(λ/4) = π/2 radians.
Correct Answer: B — π/2 radians
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Q. What is the phase difference between two points on a wave that are half a wavelength apart?
-
A.
0 radians
-
B.
π/2 radians
-
C.
π radians
-
D.
2π radians
Solution
The phase difference between two points that are half a wavelength apart is π radians.
Correct Answer: C — π radians
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Q. What is the phase difference between two points on a wave that are one wavelength apart?
-
A.
0 radians
-
B.
π/2 radians
-
C.
π radians
-
D.
2π radians
Solution
The phase difference between two points on a wave that are one wavelength apart is 2π radians.
Correct Answer: D — 2π radians
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Q. What is the phase difference between two waves that are 180° out of phase?
-
A.
0
-
B.
90°
-
C.
180°
-
D.
360°
Solution
A phase difference of 180° corresponds to the waves being out of phase, leading to destructive interference.
Correct Answer: C — 180°
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Q. What is the phase difference between two waves that are in phase?
-
A.
0 radians
-
B.
π/2 radians
-
C.
π radians
-
D.
2π radians
Solution
When two waves are in phase, their phase difference is 0 radians.
Correct Answer: A — 0 radians
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