Datasets:
File size: 12,066 Bytes
62a9c07 |
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 |
[
{
"name": "IChO-2025_5",
"background": {
"image": [
"images/5/5_bg.png"
],
"context": "Freshwater is scarce in the arid climate of the UAE. The country relies on solar-powered desalination plants to produce freshwater. A Dubai desalination plant uses a multi-stage flash (MSF) desalination process. In MSF desalination, seawater is heated by passing through a series of heat exchangers to raise its temperature, reaching its saturation temperature at a high pressure. When pressure is reduced, this superheated seawater gives off pure water vapour to become saturated again, a process known as flashing.\n Assume seawater in Dubai is at T_{0} = 25.00^{\\circ}\\mathrm{C} and is an aqueous solution of 3.45\\% mass NaCl. Assume complete ionisation of NaCl in water. The boiling point of seawater is higher than pure water. The boiling point elevation constant, K_{\\mathrm{b}} = 0.5120 \\, \\mathrm{K} \\, \\mathrm{kg} \\, \\mathrm{mol}^{-1}"
},
"points": 16
},
{
"name": "IChO-2025_5.1",
"modality": "text",
"type": "Quantitative Calculation",
"evaluation": "Numeric Verification",
"points": 2,
"field": "",
"source": "IChO-2025",
"question": {
"context": "Calculate the boiling point T (in °C) of Dubai seawater at atmospheric pressure. If you cannot calculate it, use 373.50 K for later parts."
},
"answer": [
{
"step": 1,
"content": "For 100 g solution: m(NaCl) = 3.45 g; m(H2O) = 96.55 g. M(NaCl) = 58.44 g mol^{-1}.",
"points": 0.5
},
{
"step": 2,
"content": "Molality: m = (3.45/58.44) / 0.09655 = 0.6114 mol kg^{-1}.",
"points": 0.5
},
{
"step": 3,
"content": "Assuming complete ionisation (i = 2): ΔT_b = i K_b m = 2 * 0.512 * 0.6114 = 0.6261 K.",
"points": 0.5
},
{
"step": 4,
"content": "Boiling point: T = 373.15 + 0.6261 = 373.7761 K = 100.6261 °C.",
"points": 0.5
}
]
},
{
"name": "IChO-2025_5.2",
"modality": "text",
"type": "Quantitative Calculation",
"evaluation": "Numeric Verification",
"points": 2,
"field": "",
"source": "IChO-2025",
"question": {
"context": "A solution boils at T_b = 378.00 K. Fully ionised NaCl; K_b = 0.5120 K kg mol^{-1}. Find mass percent of NaCl, w_NaCl.",
"requirement": "Use ΔT_b = i K_b m with i = 2, then solve for x g NaCl in 100 g total."
},
"answer": [
{
"step": 1,
"content": "ΔT_b = 378.00 − 373.15 = 4.85 K.",
"points": 0.5
},
{
"step": 2,
"content": "Molality: m = ΔT_b / (i K_b) = 4.85 / (2 × 0.512) = 4.736 mol kg^{-1}.",
"points": 0.5
},
{
"step": 3,
"content": "Let 100 g total: x g NaCl, (100−x) g H2O. m = (x/58.44) / ((100−x)/1000) ⇒ x ≈ 21.7 g.",
"points": 1.0
}
]
},
{
"name": "IChO-2025_5.3",
"modality": "text",
"type": "Quantitative Calculation",
"evaluation": "Numeric Verification",
"points": 3,
"field": "",
"source": "IChO-2025",
"question": {
"context": "Find the boiling point T (°C) of the initial Dubai seawater at p = 2.50 atm. Use ΔH_vap = 40.716 kJ mol^{-1}.",
"requirement": "Use Clausius–Clapeyron with T1 = 373.7761 K (from 5.1) at P1 = 1 atm: ln(P2/P1) = −ΔH_vap/R (1/T2 − 1/T1)."
},
"answer": [
{
"step": 1,
"content": "Values: T1 = 373.7761 K; P1 = 1.0 atm; P2 = 2.50 atm; ΔH_vap = 40.716 kJ mol^{-1}.",
"points": 0.5
},
{
"step": 2,
"content": "ln(2.5/1.0) = −(40716 J mol^{-1})/(8.314 J K^{-1} mol^{-1}) × (1/T2 − 1/373.7761).",
"points": 1.0
},
{
"step": 3,
"content": "Solve ⇒ T2 = 401.88 K = 128.73 °C.",
"points": 1.5
}
]
},
{
"background": {
"context": "In the plant, a flash chamber (of volume, $V = 100$ L) contains a mass of $1.00$ kg of seawater (l) at $T_{1} = 90.0^{\\circ}$C. Another mass of $1.00\\,\\mathrm{kg}$ of seawater is then overheated to $T_{2} = 110.0^{\\circ}\\mathrm{C}$ at high pressure before being added to this chamber, where a reduction in pressure causes some water to turn into steam. After equilibrium was established, the temperature in the chamber was $T_{\\mathrm{f}} = 97.0^{\\circ}\\mathrm{C}$. Assume there was no loss of energy, and that the latent heat of vaporisation is independent of temperature. The specific heat capacity of seawater, $C_{\\mathrm{p}} = 3.85\\,\\mathrm{kJ}\\,\\mathrm{kg}^{-1}\\,\\mathrm{K}^{-1}$, is assumed to be independent of temperature. The density of seawater, $d = 1025\\,\\mathrm{kg}\\,\\mathrm{m}^{-3}$."
}
},
{
"name": "IChO-2025_5.4",
"modality": "text",
"type": "Quantitative Calculation",
"evaluation": "Numeric Verification",
"points": 2,
"field": "",
"source": "IChO-2025",
"question": {
"context": "Two 1.00 kg seawater portions at 110 °C and 90 °C are mixed in a 100 L chamber; equilibrium T_f = 97 °C. Find moles of water vapourised, n. Assume no heat loss; Cp(seawater)=3.85 kJ kg^{-1} K^{-1}; E_vap=2260 kJ kg^{-1}; vapour Cp negligible.",
"requirement": "Set heat lost on cooling equal to latent heat of vaporisation."
},
"answer": [
{
"step": 1,
"content": "Let n be moles vaporised; mass vaporised = 0.018016 n kg.",
"points": 0.5
},
{
"step": 2,
"content": "Heat lost on cooling: Q_c = (2 − 0.018016 n) kg × 3850 J kg^{-1} K^{-1} × (373.15 − 370.15) K ≈ 23100 − 208.0848 n J mol^{-1}.",
"points": 0.5
},
{
"step": 3,
"content": "Heat to vaporise: Q_v = (0.018016 n) kg × 2260×10^3 J kg^{-1} = 40716.16 n J.",
"points": 0.5
},
{
"step": 4,
"content": "Energy balance Q_c = Q_v ⇒ 23100 = 40924.24 n ⇒ n = 0.565 mol.",
"points": 0.5
}
]
},
{
"name": "IChO-2025_5.5",
"modality": "text",
"type": "Quantitative Calculation",
"evaluation": "Numeric Verification",
"points": 2,
"field": "",
"source": "IChO-2025",
"question": {
"context": "A 100 L chamber initially at 90 °C contains vapour at p_i = 0.690 atm above ~1 L liquid. After adding overheated water and flashing, n_vap from 5.4 is produced and the final temperature is 97 °C. Find final vapour pressure p_f (atm), assuming ideal gas.",
"requirement": "Use V_vap ≈ 0.099 m^3; pV = nRT."
},
"answer": [
{
"step": 1,
"content": "Initial vapour moles: n_0 = p_i V / (R T) = (0.690×101325 Pa × 0.099 m^3) / (8.314 J K^{-1} mol^{-1} × 363.15 K) = 2.292 mol.",
"points": 1.0
},
{
"step": 2,
"content": "After flashing: n = n_0 + n_vap = 2.292 + 0.565 = 2.857 mol.",
"points": 0.5
},
{
"step": 3,
"content": "Final pressure: p_f = nRT/V = (2.857 mol × 8.314 × 370.15 K) / 0.099 m^3 = 8.9716×10^4 Pa = 0.885 atm.",
"points": 0.5
}
]
},
{
"name": "IChO-2025_5.6",
"modality": "text",
"type": "Quantitative Calculation",
"evaluation": "Numeric Verification",
"points": 2,
"field": "",
"source": "IChO-2025",
"question": {
"context": "Find the thermal energy E (kWh) to heat 1.00 kg seawater from 25.0 °C to 110.0 °C. Cp = 3.85 kJ kg^{-1} K^{-1}.",
"requirement": "Compute Q = m C_p ΔT and convert kJ to kWh (1 kWh = 3600 kJ)."
},
"answer": [
{
"step": 1,
"content": "ΔT = 110 − 25 = 85 °C.",
"points": 0.5
},
{
"step": 2,
"content": "Q = 1.00 kg × 3.85 kJ kg^{-1} K^{-1} × 85 K = 327.25 kJ.",
"points": 1.0
},
{
"step": 3,
"content": "E = 327.25/3600 = 0.0909 kWh.",
"points": 0.5
}
]
},
{
"name": "IChO-2025_5.7",
"modality": "text",
"type": "Quantitative Calculation",
"evaluation": "Numeric Verification",
"points": 1,
"field": "",
"source": "IChO-2025",
"question": {
"context": "The plant makes 50,000 m^3 pure water per day and extracts 85% of water from feed. Find daily mass of Dubai seawater required (kg). Assume ρ = 1000 kg m^{-3} for water and seawater contains 3.45% NaCl by mass.",
"requirement": "Account for extraction efficiency and water fraction in seawater (0.9655)."
},
"answer": [
{
"step": 1,
"content": "Mass of pure water needed in feed: 50,000 m^3 × 1000 kg m^{-3} / 0.85 = 5.88 × 10^7 kg.",
"points": 0.5
},
{
"step": 2,
"content": "Mass of seawater required: (5.88 × 10^7 kg)/0.9655 = 6.09 × 10^7 kg.",
"points": 0.5
}
]
},
{
"background": {
"context": "Plants make efficient use of heat exchangers to save energy. We can assume the total energy required by the plant is the same as the energy needed to heat all the seawater from T_{1} = 25.0^{\\circ}\\mathrm{C} to T_{2} = 110.0^{\\circ}\\mathrm{C}."
}
},
{
"name": "IChO-2025_5.8",
"modality": "text",
"type": "Quantitative Calculation",
"evaluation": "Numeric Verification",
"points": 2,
"field": "",
"source": "IChO-2025",
"question": {
"context": "Assume the plant's net energy equals heating all seawater from 25.0 °C to 110.0 °C (use result of 5.6 per kg). A 10 m^2 solar panel supplies 2.00 kW averaged over 12 h per day and system efficiency is 67%. Find number of panels N.",
"requirement": "Use mass from 5.7 and E_per_kg = 0.0909 kWh."
},
"answer": [
{
"step": 1,
"content": "Total energy required: E_req = (6.09 × 10^7 kg) × 0.0909 kWh = 5.536 × 10^6 kWh.",
"points": 0.5
},
{
"step": 2,
"content": "Accounting for 67% efficiency: E_need_from_panels = 5.536 × 10^6 / 0.67 = 8.263 × 10^6 kWh.",
"points": 0.75
},
{
"step": 3,
"content": "Energy per panel per day: 2.00 kW × 12 h = 24 kWh. Panels needed: N = (8.263 × 10^6) / 24 = 3.44292 × 10^5 ≈ 344,292.",
"points": 0.75
}
]
}
]
|