| Step 1: Calculate the moles of HCl. | Volume = 600 mL = 0.6 L; Molarity = 0.04 M; Moles HCl = Volume × Molarity = 0.6 × 0.04 = 0.024 mol. |
| Step 2: Calculate the moles of H2SO4. | Volume = 400 mL = 0.4 L; Molarity = 0.02 M; Moles H2SO4 = Volume × Molarity = 0.4 × 0.02 = 0.008 mol. |
| Step 3: Determine total moles of H+ ions. | HCl dissociates fully, providing 1 mol of H+ per mol of HCl: Moles of H+ from HCl = 0.024 mol; H2SO4 dissociates to provide 2 mol of H+ per mol: Moles of H+ from H2SO4 = 2 × 0.008 = 0.016 mol; Total moles of H+ = 0.024 + 0.016 = 0.040 mol. |
| Step 4: Calculate the total volume of the solution. | Total volume = 600 mL + 400 mL = 1000 mL = 1 L. |
| Step 5: Calculate the final concentration of H+ ions. | [H+] = Total moles of H+ / Total volume = 0.040 mol / 1 L = 0.040 M. |
| Step 6: Calculate the pH of the solution. | pH = -log[H+] = -log(0.040) ≈ 1.40. |
| Verification: The calculated pH ≈ 1.4 falls exactly within the given range (1.4, 1.4). |
An ideal massless spring \( S \) can be compressed \( 1 \) m by a force of \( 100 \) N in equilibrium. The same spring is placed at the bottom of a frictionless inclined plane inclined at \( 30^\circ \) to the horizontal. A \( 10 \) kg block \( M \) is released from rest at the top of the incline and is brought to rest momentarily after compressing the spring by \( 2 \) m. If \( g = 10 \) m/s\( ^2 \), what is the speed of the mass just before it touches the spring?
