10.0 g of a metal, initially at 25°C, are placed into 10.0 g of water, initially
ID: 950747 • Letter: 1
Question
10.0 g of a metal, initially at 25°C, are placed into 10.0 g of water, initially at 100°C. Which metal will have the highest final temperature? Shown after each metal is its specific heat in J/(g °C).
magnesium 1.020
sulfur 0.73
zinc 0.39
mercury 0.14
A reaction for which H° = + 98.8 kJ and S° = + 141.5 J/K is _______________(spontaneous or nonspontaneous) at low temperatures and _________________ (spontaneous or nonspontaneous) at high temperatures.
a.magnesium 1.020
b.sulfur 0.73
c.zinc 0.39
d.mercury 0.14
Explanation / Answer
a.
magnesium 1.020
b.
sulfur 0.73
c.
zinc 0.39
d.
mercury 0.14
In order to find the final temperature, or the temperature at equilibrium, set the heat capacity for the metal and the water equal, except Q for water is negative because it loses heat energy.
Qmetal=Qwater (The negative sign indicates that the water loses heat energy.)
mc(TfTi)=mc(TfTi)
A
Magnesium
10 x 1.020 ( T - 25) = - 10 x 4.186 ( T - 100)
10.2 T -255 = - 41.86 T +4186
52.06 T = 4441
T = 85.3 °C
B) Sulfur
10 x 0.73 ( T - 25) = - 10 x 4.186 ( T - 100)
7.3 T -182.5 = - 41.86 T +4186
49.16 T = 4368.5
T = 88.86 °C
C) zinc
10 x 0.39 ( T - 25) = - 10 x 4.186 ( T - 100)
3.9 T -97.5 = - 41.86 T +4186
45.76 T = 4283.5
T = 93.6 °C
D) Mercury
10 x 0.14 ( T - 25) = - 10 x 4.186 ( T - 100)
1.4 T -35 = - 41.86 T +4186
43.26 T = 4221
T = 97.5 °C
So the Mercury has highest final temperature.
A reaction for which H° = + 98.8 kJ and S° = + 141.5 J/K is nonspontaneous at low temperatures and spontaneous at high temperatures.
a.
magnesium 1.020
b.
sulfur 0.73
c.
zinc 0.39
d.
mercury 0.14
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