1. A 48.0g sample of an unknown metal at 99°C was placed in a constant-pressure
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Question
1. A 48.0g sample of an unknown metal at 99°C was placed in a constant-pressure calorimeter containing 70.0 g of water at 24.0°C. The final temperature of the system was found to be 28.4°C. Calculate the specific heat of the metal. (The heat capacity of the calorimeter is 10.4 J/°C.)2.A balloon 19.0 m in diameter is inflated with helium at 23°C. Calculate the work done (in kJ) during the inflation process if the atmospheric pressure is 97.7 kPa.
3.Ice at 0.0°C is placed in a Styrofoam cup containing 360 g of a soft drink at 25.8°C. The specific heat of the drink is about the same as that of water. Some ice remains after the ice and soft drink reach an equilibrium temperature of 0.0°C. Determine the mass of ice that has melted. Ignore the heat capacity of the cup. (Hint: It takes 334 J to melt 1 g of ice at 0.0°C.)
4. When 1.049 g of naphthalene (C10H8) is burned in a constant-volume bomb calorimeter at 298 K, 42.16 kJ of heat is evolved. Calculate U and w for the reaction on a molar basis. 1. A 48.0g sample of an unknown metal at 99°C was placed in a constant-pressure calorimeter containing 70.0 g of water at 24.0°C. The final temperature of the system was found to be 28.4°C. Calculate the specific heat of the metal. (The heat capacity of the calorimeter is 10.4 J/°C.)
2.A balloon 19.0 m in diameter is inflated with helium at 23°C. Calculate the work done (in kJ) during the inflation process if the atmospheric pressure is 97.7 kPa.
3.Ice at 0.0°C is placed in a Styrofoam cup containing 360 g of a soft drink at 25.8°C. The specific heat of the drink is about the same as that of water. Some ice remains after the ice and soft drink reach an equilibrium temperature of 0.0°C. Determine the mass of ice that has melted. Ignore the heat capacity of the cup. (Hint: It takes 334 J to melt 1 g of ice at 0.0°C.)
4. When 1.049 g of naphthalene (C10H8) is burned in a constant-volume bomb calorimeter at 298 K, 42.16 kJ of heat is evolved. Calculate U and w for the reaction on a molar basis.
2.A balloon 19.0 m in diameter is inflated with helium at 23°C. Calculate the work done (in kJ) during the inflation process if the atmospheric pressure is 97.7 kPa.
3.Ice at 0.0°C is placed in a Styrofoam cup containing 360 g of a soft drink at 25.8°C. The specific heat of the drink is about the same as that of water. Some ice remains after the ice and soft drink reach an equilibrium temperature of 0.0°C. Determine the mass of ice that has melted. Ignore the heat capacity of the cup. (Hint: It takes 334 J to melt 1 g of ice at 0.0°C.)
4. When 1.049 g of naphthalene (C10H8) is burned in a constant-volume bomb calorimeter at 298 K, 42.16 kJ of heat is evolved. Calculate U and w for the reaction on a molar basis. 4. When 1.049 g of naphthalene (C10H8) is burned in a constant-volume bomb calorimeter at 298 K, 42.16 kJ of heat is evolved. Calculate U and w for the reaction on a molar basis.
Explanation / Answer
1. We know
heat lost by metal = heat gained by water + heat gained by calorimeter …(1)
[Heat (Q) = mass(m) * specific heat capacity(Cp )* Temperature difference (T)]….(2)
Given, specific heat capacity of water = Cp,water = 4.184J/gºC
Heat capacity of the calorimeter = 10.4 J/°C
mmetal = 48.0g
mwater = 70.0g
Intial Temperature of metal (Ti,metal)= 99.0°C
Intial Temperature of calorimeter/water (Ti) = 24.0°C
Final Temperature of calorimeter/water/metal (Tf) = 28.4°C
From equation (1),
- mmetal*Cp,metal*(Tf-Ti,metal)= [mwater*Cp,water+Cp,calorimeter](Tf-Ti)
-48.0g* Cp,metal*(28.4°C - 99.0°C)= [70.0g*4.184J/gºC+10.4 J/°C]*(28.4°C -24.0°C)
Hence specific heat of the metal is 0.394 J/gºC
2. Before inflation, the volume of the balloon is zero. [Vi = 0]
Let suppose balloon as a spherical shape.
Final volume (Vf) = 4/3 r3
Given, diameter of balloon (d) = 19.0 m
Radius of balloon (r) = d/2 = 9.5 m
i.e. Vf = 4/3 (9.5m)3 = 3589.54 m3
Pext = 97.7 kPa = 97.7*103 Pa
Work done = -PextV = -Pext(Vf-Vi) = -(97.7*103 Pa)( 3589.54 m3 -0)
= -350698.058*103 Pa-m3 =-350698.058*103 J
= -350698.058 kJ ~ -3.507*105 kJ
{negative sign indicates the work is done by the system.}
Hence the work done is 3.507*105 kJ
3. Here, all the heat lost by the soft-drink is gain by the ice. So,
heat gained by ice = heat lost by soft-drink …..(1)
Qice = mice*Hfus
Qsoft-drink =msoft-drink*Cp*T
Putting these in (1)
mice*Hfus = -msoft-drink*Cp*T [negative sign for heat loss]…(2)
We know,
specific heat capacity of water = Cp,water = 4.184J/gºC =specific heat capacity of soft-drink
Given, Hfus = 334 J [It takes 334 J to melt 1 g of ice at 0.0°C. This is known as heat of fussion]
Ti = 25.8°C
Tf = 0.0°C
msoft-drink = 360g
Putting the above values in (2)
mice*334 J = -360g*4.184J/gºC*(0.0°C - 25.8°C)
=> mice = (360g*4.184J/gºC*25.8°C)/( 334 J)
=> mice = 116.35g
Hence, mass of ice that has melted is 116.35 g
4. According to the first law of thermodynamics
U = q + w ……………(1)
Where, w= work done = -PextV
Here, volume is constant. So, V = 0
Hence, w = 0
Now, equation (1) become
U = q
Given, heat evolved (q) = -42.16 kJ [negative sign indicates the heat evolved from the system]
U = -42.16 kJ
On the molar basis,
Molar mass of naphthalene (C10H8) = 128 g/mol
Mass of naphthalene given = 1.049 g
U = (-42.16 kJ*128 g/mol)/(1.049 g) = -5144.40 kJ/mol (negative sign indicates the heat lost from the system)
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