A mass of 34.05 g of H2O(s) at 273 K is dropped into 185 g of H2O(l) at 310. K in an insulated container at 1 bar of pressure. Calculate the temperature of the system once equi- librium has been reached. Assume that CP, m for H2O is con- stant at its values for 298 K throughout the temperature range of interest.
Answers
Answer:
The temperature of the system once equilibrium is reached, is 292 Kelvin
Explanation:
Step 1: Data given
Mass of H2O = 34.05 grams
⇒ temperature = 273 K
Mass of H2O at 310 K = 185 grams
Pressure = 1 bar = 0.9869 atm
Step 2: Calculate the final temperature
n(ice)*ΔH(ice fusion) + n(ice)*CP(H2O)(Tfinal- Ti,ice) + n(H20)*CP(H2O)*(Tfinal-Ti,H2O) = 0
Tfinal = [n(ice)*CP(ice)*Ti(ice) + n(H2O)*CP(H2O)*Ti(H20) - n(ice)*ΔH(ice fusion)] / [n(ice)*CP(ice) +n(H2O)*CP(H2O)]
⇒ with n(ice) = moles of ice = 34.05 grams / 18.02 g/mol = 1.890 moles
⇒ with CP(ice) = 75.3 J/K*mol
⇒ with Ti(ice) = the initial temperature of ice = 273 K
⇒ with n(H2O) = the moles of water = 185.0 grams / 18.02 g/mol = 10.27 moles
⇒ with CP(H2O) = CP(ice) = 75.3 J/K*mol
⇒ with Ti(H2O) = the initial temperature of the water = 310 K
⇒ with ΔH(ice, fusion) = 6010 J/mol
Tfinal = [1.890 moles * 75.3 J/K*mol * 273 + 10.27 mol * 75.3 J/K*mol * 310 K - 1.890 moles * 6010 J/mol] / [1.890 moles *75.3J/k*mol + 10.27 mol * 75.3 J/K*mol]
38852.541 + 239732.61 - 11358.9 = 267226.251
Tfinal= 291.8 ≈ 292 Kelvin
The temperature of the system once equilibrium is reached, is 292 Kelvin
Final answer:
We must use the principle of conservation of energy to equate the heat gained by the ice to the heat lost by the water, in a given equation, to calculate the final equilibrium temperature.
Explanation:
The topic here is thermodynamics, specifically calculating the final equilibrium temperature when two substances are mixed. Given the information, we can apply the principle of conservation of energy, which in this context is the heat gained by one substance is equal to the heat lost by the other. In this case, the heat gained by the ice (H2O(s)) as it melts and increases in temperature is equal to the heat lost by the water (H2O(l)). Therefore, we have the equation 34.05 g * 1 kcal/kg * K *(T - 273 K) + 34.05 g * 80 Cal/g = 185 g * 1 kcal/kg*K *(310 K - T) where T is the final temperature to be solved.
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b) A graph of the relationship is attached as an image.
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Wavelength is defined as the distance between identical points or adjacent crests in the adjacent cycles of a waveform signal propagated in the space or wires.
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b} The exact time when an individual atom will decay can be accurately predicted.
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Answers
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Rate law expression for first order kinetics is given by:
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Expression for calculating half life, which is the time taken by the half of the reactants to decompose is:
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