Q. What is the value of the equilibrium constant Kc for the reaction A + B ⇌ C + D at 25°C if the concentrations are [A]=0.1 M, [B]=0.2 M, [C]=0.3 M, [D]=0.4 M?
A.
0.5
B.
1.0
C.
2.0
D.
4.0
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Solution
Kc = ([C][D]) / ([A][B]) = (0.3 * 0.4) / (0.1 * 0.2) = 2.0
Correct Answer: C — 2.0
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Q. What is the value of the equilibrium constant Kc for the reaction A + B ⇌ C at 25°C if the concentrations are [A] = 0.1 M, [B] = 0.2 M, and [C] = 0.3 M?
A.
0.5
B.
1.0
C.
1.5
D.
2.0
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Solution
Kc = [C]/([A][B]) = 0.3/(0.1*0.2) = 1.5
Correct Answer: B — 1.0
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Q. What is the value of the equilibrium constant Kc for the reaction: 2A ⇌ B + C if at equilibrium [A] = 0.5 M, [B] = 0.2 M, and [C] = 0.3 M?
A.
0.12
B.
0.30
C.
0.60
D.
1.20
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Solution
Kc = [B][C] / [A]^2 = (0.2)(0.3) / (0.5)^2 = 0.12 / 0.25 = 0.48.
Correct Answer: C — 0.60
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Q. What is the value of the equilibrium constant Kp for the reaction 2NO2(g) ⇌ N2O4(g) at a certain temperature?
A.
Kp = (P_N2O4) / (P_NO2)^2
B.
Kp = (P_NO2)^2 / (P_N2O4)
C.
Kp = (P_N2O4)^2 / (P_NO2)
D.
Kp = (P_NO2) / (P_N2O4)^2
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Solution
Kp is defined as the partial pressure of products over reactants, raised to the power of their coefficients.
Correct Answer: A — Kp = (P_N2O4) / (P_NO2)^2
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Q. What is the value of the equilibrium constant Kp for the reaction: N2(g) + 3H2(g) ⇌ 2NH3(g) at 25°C?
A.
0.5
B.
1.0
C.
0.1
D.
Depends on the initial concentrations
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Solution
The value of Kp is specific to the reaction conditions and cannot be determined without knowing the initial concentrations or the extent of the reaction.
Correct Answer: D — Depends on the initial concentrations
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Q. What is the value of the gas constant R in L·atm/(K·mol)?
A.
0.0821
B.
8.314
C.
0.08314
D.
1.987
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Solution
The gas constant R is 0.0821 L·atm/(K·mol).
Correct Answer: A — 0.0821
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Q. What is the value of the gravitational constant G?
A.
6.67 x 10^-11 N(m/kg)^2
B.
9.81 m/s^2
C.
3.00 x 10^8 m/s
D.
1.60 x 10^-19 C
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Solution
The gravitational constant G is approximately 6.67 x 10^-11 N(m/kg)^2.
Correct Answer: A — 6.67 x 10^-11 N(m/kg)^2
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Q. What is the value of the integral ∫(0 to 1) (3x^2 + 2)dx?
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Solution
Integral = [x^3 + 2x] from 0 to 1 = (1 + 2) - (0) = 3.
Correct Answer: A — 5/3
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Q. What is the value of the integral ∫(0 to 1) (3x^2)dx?
A.
1
B.
1/3
C.
1/2
D.
3/4
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Solution
The integral evaluates to [x^3] from 0 to 1 = 1^3 - 0^3 = 1.
Correct Answer: A — 1
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Q. What is the value of the integral ∫(0 to 1) x^2 dx?
A.
1/3
B.
1/2
C.
1/4
D.
1
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Solution
The integral ∫(0 to 1) x^2 dx = [x^3/3] from 0 to 1 = 1/3.
Correct Answer: A — 1/3
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Q. What is the value of the integral ∫(1 to 2) (3x^2 - 2)dx?
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Solution
The integral evaluates to [x^3 - 2x] from 1 to 2 = (8 - 4) - (1 - 2) = 3.
Correct Answer: B — 4
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Q. What is the value of the integral ∫(1 to 2) (x^2 + 2x)dx?
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Solution
The integral evaluates to 7.
Correct Answer: A — 7
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Q. What is the value of the integral ∫(1/(x^2 + 1))dx?
A.
tan^-1(x) + C
B.
sin^-1(x) + C
C.
cos^-1(x) + C
D.
ln(x) + C
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Solution
The integral evaluates to tan^-1(x) + C.
Correct Answer: A — tan^-1(x) + C
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Q. What is the value of the integral ∫(2x + 3)dx from 0 to 1?
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Solution
The integral ∫(2x + 3)dx = [x^2 + 3x] from 0 to 1 = (1^2 + 3*1) - (0 + 0) = 1 + 3 = 4.
Correct Answer: B — 3
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Q. What is the value of the integral ∫(2x)dx from 0 to 1?
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Solution
∫(2x)dx = x^2 from 0 to 1 = 1^2 - 0^2 = 1.
Correct Answer: A — 1
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Q. What is the value of the integral ∫(2x)dx from 0 to 2?
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Solution
∫(2x)dx = x^2 from 0 to 2 = 2^2 - 0^2 = 4.
Correct Answer: A — 4
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Q. What is the value of the integral ∫(2x^3 - 3x^2 + 4)dx from 1 to 2?
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Solution
The integral evaluates to [0.5x^4 - x^3 + 4x] from 1 to 2 = (8 - 8 + 8) - (0.5 - 1 + 4) = 8 - 2.5 = 5.5.
Correct Answer: B — 6
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Q. What is the value of the integral ∫(2x^3 - 3x^2 + 4)dx from 1 to 3?
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Solution
The integral evaluates to 20.
Correct Answer: B — 20
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Q. What is the value of the integral ∫_0^1 (3x^2 + 2x) dx?
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Solution
Evaluating the integral gives [x^3 + x^2]_0^1 = (1 + 1) - (0 + 0) = 2.
Correct Answer: B — 2
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Q. What is the value of the limit lim (x -> 0) (sin(5x)/x)?
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Solution
Using L'Hôpital's rule, the limit evaluates to 5.
Correct Answer: C — 5
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Q. What is the value of the limit lim (x -> 1) (x^2 - 1)/(x - 1)?
A.
0
B.
1
C.
2
D.
Infinity
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Solution
Using L'Hôpital's Rule, the limit evaluates to 2.
Correct Answer: C — 2
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Q. What is the value of the limit lim(x->0) (sin(x)/x)?
A.
0
B.
1
C.
∞
D.
undefined
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Solution
The limit lim(x->0) (sin(x)/x) = 1.
Correct Answer: B — 1
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Q. What is the value of the limit lim(x→0) (sin(5x)/x)?
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Solution
Using L'Hôpital's rule, the limit evaluates to 5.
Correct Answer: C — 5
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Q. What is the value of the limit lim(x→0) (sin(x)/x)?
A.
0
B.
1
C.
∞
D.
undefined
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Solution
The limit lim(x→0) (sin(x)/x) = 1.
Correct Answer: B — 1
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Q. What is the value of the limit: lim (x -> ∞) (1/x)?
A.
0
B.
1
C.
Infinity
D.
Undefined
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Solution
As x approaches infinity, 1/x approaches 0.
Correct Answer: A — 0
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Q. What is the value of the principal quantum number (n) for an electron in the 4f subshell?
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Solution
The principal quantum number n for the f subshell is 4.
Correct Answer: B — 4
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Q. What is the value of the principal quantum number (n) for an electron in the 4s orbital?
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Solution
The principal quantum number (n) indicates the energy level of the electron. For 4s, n=4.
Correct Answer: D — 4
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Q. What is the value of the principal quantum number (n) for an electron in the ground state of a hydrogen atom?
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Solution
In the ground state, the electron is in the first energy level, which corresponds to n=1.
Correct Answer: B — 1
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Q. What is the value of the principal quantum number (n) for the outermost electrons in a sodium atom?
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Solution
Sodium has an atomic number of 11, and its electron configuration is 1s² 2s² 2p⁶ 3s¹. The outermost electrons are in n=3.
Correct Answer: C — 3
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Q. What is the value of the principal quantum number (n) for the outermost electron in potassium (K)?
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Solution
Potassium has the electronic configuration [Ar] 4s1, so the outermost electron is in n=4.
Correct Answer: B — 4
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