1. What is the change in internal energy (in J) of a system that absorbs 0.677 kJ of heat from its surroundings and has 0.438 kcal of work done on it?
2. A 30.5 g sample of an alloy at 94.0°C is placed into 48.7 g water at 20.3°C in an insulated coffee cup. The heat capacity of the coffee cup (without the water) is 9.2 J/K. If the final temperature of the system is 31.1°C, what is the specific heat capacity of the alloy? (c of water is 4.184 J/g×K)
3. When 33.5 mL of 0.535 M H2SO4 is added to 33.5 mL of 1.07 M KOH in a coffee-cup calorimeter at 23.50°C, the temperature rises to 30.17°C. Calculate H of this reaction per mole of H2SO4 and KOH reacted. (Assume that the total volume is the sum of the individual volumes and that the density and specific heat capacity of the solution are the same as for pure water: d = 1.00 g/mL and c = 4.184 J/g×K.)
4. Organic hydrogenation reactions, in which H2 and an "unsaturated" organic compound combine, are used in the food, fuel, and polymer industries. In the simplest case, ethene (C2H4) and H2 form ethane (C2H6). If 124 kJ is given off per mole of C2H4 reacting, how much heat is released when 14.6 kg of C2H6 forms?
Can someone please explain how to do these problems ?
Sure! I'd be happy to explain how to solve these problems. Let's go through each one step by step:
1. To find the change in internal energy of a system, we need to use the first law of thermodynamics, which states that the change in internal energy (∆U) is equal to the heat added (q) minus the work done (w) on the system.
In this case, we have:
q = 0.677 kJ (convert to J by multiplying by 1000)
w = 0.438 kcal (convert to J by multiplying by 4184)
So, we can calculate ∆U as follows:
∆U = q - w
= (0.677 kJ * 1000 J/kJ) - (0.438 kcal * 4184 J/kcal)
2. This problem involves finding the specific heat capacity of an alloy. The heat gained by the alloy is equal to the heat lost by the water, based on the principle of energy conservation. We can use the formula:
Heat gained by alloy = Heat lost by water
The heat gained by the alloy can be calculated by:
q_alloy = mass_alloy * specific heat capacity_alloy * ∆T
The heat lost by the water can be calculated by:
q_water = mass_water * specific heat capacity_water * ∆T
Since the coffee cup is insulated, there is no heat exchange with the surroundings, so:
q_alloy = -q_water
By rearranging the equation, we can obtain the specific heat capacity of the alloy as follows:
specific heat capacity_alloy = (mass_water * specific heat capacity_water * ∆T) / (mass_alloy * ∆T)
3. This problem involves calculating the enthalpy change (ΔH) of a reaction using calorimetry. Calorimetry is a technique used to measure the amount of heat exchanged during a chemical or physical process.
To calculate ΔH, we can use the equation:
ΔH = q / moles
First, we need to calculate the heat exchanged (q) by using the formula:
q = mass_solution * specific heat capacity_solution * ∆T
Then, we can determine the moles of H2SO4 and KOH reacted by using the equations:
moles_H2SO4 = concentration_H2SO4 * volume_H2SO4
moles_KOH = concentration_KOH * volume_KOH
Finally, we can calculate ΔH by dividing q by the sum of the moles:
ΔH = q / (moles_H2SO4 + moles_KOH)
4. This problem involves calculating the heat released in a reaction using the enthalpy change (∆H) per mole. The given value of 124 kJ/mol represents the ∆H for the reaction C2H4 + H2 → C2H6.
To calculate the heat released when 14.6 kg of C2H6 forms, we need to convert the mass of C2H6 to moles using its molar mass. Then, we can multiply the number of moles by the ∆H value to obtain the heat released.
I hope this helps! Let me know if you have any further questions.