Daily Practice Questions

Explanation: Moles of $HNO_3$ are calculated as $0.20\text{ L} \times 0.30\text{ M} = 0.060\text{ mol}$. The stoichiometric ratio is 8 mol $HNO_3$ to 3 mol Cu. Since 0.060 mol acid requires only 0.0225 mol Cu, the 0.30 mol Cu is in excess, making $HNO_3$ the limiting reactant. The moles of $NO$ produced are determined by the 8:2 ratio (or 4:1), so $0.060\text{ mol } HNO_3 \times (2\text{ mol } NO / 8\text{ mol } HNO_3) = 0.015\text{ mol}$.

Explanation: For any object in a stable circular orbit, the magnitude of its gravitational potential energy ($U$) is exactly twice its kinetic energy ($KE$), but with an opposite sign because $U$ is negative while $KE$ is positive. This relationship arises from the virial theorem for inverse-square force laws, where the total mechanical energy is half the potential energy ($E = U/2$). Since the total energy is also the sum of kinetic and potential energies ($E = KE + U$), substituting $U = -2KE$ satisfies the condition that the total energy equals $-KE$.

Explanation: The postcondition should be a true assertion about the major action of the segment. The segment overwrites the elements of array a with the nonnegative elements of a . Then n is adjusted so that now the array a[0]…a[n-1] contains just nonnegative integers. Note that even though choice E is a correct assertion about the program segment, it’s not a good postcondition because it doesn’t describe the main modification to array a (namely, all negative integers have been removed).

Explanation: By definition of logarithms, if log₃ x = 5, then 3⁵ = x. Calculating 3⁵ gives 243. Thus, x = 243.

Explanation: We have A:B = 3:7, B:C = 14:5, C:D = 15:11. First, combine A:B and B:C. Since B is common, make B equal: LCM of 7 and 14 is 14. So A:B = 6:14 (multiply by 2), and B:C = 14:5. So A:B:C = 6:14:5. Now combine with C:D = 15:11. Since C=5 in the ratio, and C=15 in the other, multiply A:B:C by 3 to get C=15: A:B:C = 18:42:15. Then D=11 (from C:D=15:11). So A:D = 18:11? Wait—C:D=15:11, so if C=15, D=11. So A:D = 18:11. But options are 1:2, 2:3, etc. Did I misread? A:B=3:7 → A/B=3/7. B:C=14:5 → B/C=14/5 → C/B=5/14. So A/C = (A/B)*(B/C) = (3/7)*(14/5)=6/5. So A:C=6:5. Now C:D=15:11 → C/D=15/11 → D/C=11/15. So A/D = (A/C)*(C/D) = (6/5)*(15/11)=18/11. So A:D=18:11, not in options. Wait—maybe B:C is 14:5 means B/C=14/5? Yes. But let's compute numerically: Let A=3k, B=7k (from A:B=3:7). From B:C=14:5, so 7k/C=14/5 → C=(7k*5)/14= (35k)/14=2.5k=5k/2. From C:D=15:11, so (5k/2)/D=15/11 → D=(5k/2)*(11/15)= (55k)/(30)=11k/6. So A=3k, D=11k/6 → A:D=3k : 11k/6 = 18:11. Not in options. But existing_answer is B (2:3). Did I misread ratios? Maybe A:B=3:7 means A/B=7/3? No, standard is first:second = A:B. Alternative interpretation: maybe the ratios are A to B is 3 to 7, so A=3a, B=7a. B:C=14:5 → 7a:C=14:5 → C=(7a*5)/14=2.5a. C:D=15:11 → 2.5a:D=15:11 → D=(2.5a*11)/15= (27.5a)/15=11a/6. So A:D=3a : 11a/6 = 18:11. Still not matching options. Unless the problem says A:B=7:3? Then A=7a, B=3a. B:C=14:5 → 3a/C=14/5 → C=15a/14. C:D=15:11 → (15a/14)/D=15/11 → D=(15a/14)*(11/15)=11a/14. So A:D=7a : 11a/14 = 98:11. No. Maybe B:C=5:14? Then B/C=5/14 → C=14B/5. A:B=3:7 → B=7A/3. So C=14*(7A/3)/5=98A/15. C:D=15:11 → (98A/15)/D=15/11 → D=(98A/15)*(11/15)=1078A/225. A:D=225:1078, no. Alternatively, perhaps the ratios are chained differently. Let's try to find A:D directly: A/B=3/7, B/C=14/5, C/D=15/11. So A/D = (A/B)*(B/C)*(C/D) = (3/7)*(14/5)*(15/11). Compute: 3*14*15 / (7*5*11) = (630)/(385) = 126/77 = 18/11. So A:D=18:11. Not in options. But existing_answer is B (2:3). Maybe the problem has a typo? Let's check if A:D=2:3 is possible. Suppose A=2, D=3. Then from C:D=15:11, C= (15/11)*3=45/11. From B:C=14:5, B= (14/5)*C= (14/5)*(45/11)=126/11. From A:B=3:7, A/B=3/7 → A= (3/7)B= (3/7)*(126/11)=54/11 ≠2. So no. Unless the ratios are reversed: B:A=3:7, etc. If A:B=7:3 (i.e., A/B=7/3), B:C=5:14, C:D=11:15. Then A/D=(7/3)*(5/14)*(11/15)= (385)/(630)=11/18. Still not 2:3. Try A:D=2:3 → A/D=2/3. Compute (A/B)*(B/C)*(C/D)= (3/7)*(14/5)*(15/11)=18/11≠2/3. So no match. But perhaps the problem meant A:B=3:7, B:C=5:14 (not 14:5), and C:D=15:11. Then A/B=3/7, B/C=5/14 → C/B=14/5. So A/C=(3/7)*(5/14)=15/98. Then C/D=15/11 → A/D=(15/98)*(15/11)=225/1078. No. Alternatively, if B:C=14:5 means C:B=14:5? Unlikely. Given standard interpretation, answer should be 18:11, not listed. But existing_answer is B (2:3). Let's see if any option fits with common mistake. Common error: multiply numerators and denominators separately: A:C = 3*15 : 7*? Wait—A:B=3:7, B:C=14:5 → A:C = 3*14 : 7*5? No, correct is A:B:C = 3*14 : 7*14 : 7*5? No—standard chain: A/B * B/C = A/C → (3/7)*(14/5)=6/5, so A:C=6:5. Then C:D=15:11 → A:D = 6*15 : 5*11? No—A/C=6/5, C/D=15/11 → A/D = (6/5)*(15/11)=18/11. If someone does A:C=3:7 * 14:5 = 42:35=6:5, then A:D=6*15 : 5*11=90:55=18:11. Still same. Maybe the problem has a typo and C:D=5:11? Then A/D=6/5 * 5/11=6/11. Not in options. Or if B:C=7:5? Then A:B=3:7, B:C=7:5 → A:B:C=3:7:5. C:D=15:11 → multiply first by 3: A:B:C=9:21:15, so D=11 → A:D=9:11. Not in options. If C:D=3:11? Then A:D=9*3 : 5*11=27:55. No. Wait—maybe the answer is B (2:3) if ratios are different. Let's solve for A:D=2:3. Set A=2k, D=3k. From C:D=15:11 → C= (15/11)*3k=45k/11. From B:C=14:5 → B= (14/5)*C= (14/5)*(45k/11)=126k/11. From A:B=3:7 → A/B=3/7 → 2k / (126k/11) = 22/126=11/63 ≠ 3/7. So impossible. Given this, the existing answer is likely wrong. But since the question is provided with existing_answer=B, and we must validate, we note discrepancy.

Explanation: The correct answer is (B) because enzymes are biological catalysts that accelerate chemical reactions without being consumed, and while most are proteins, certain RNA molecules known as ribozymes also possess catalytic activity. Choice (A) is incorrect because enzymes lower activation energy but cannot alter the overall free energy change ($\Delta G$) to make an endergonic reaction exergonic. Similarly, choice (C) is false since optimal pH varies by enzyme depending on its specific environment, and choice (D) contradicts the fundamental definition of a catalyst, which remains unchanged after the reaction.