A 15.7g block of an unknown metal is warmed to 53.2o C and plunged into an insulated beaker containing 32.5g of water initially at 24.5o C. The metal block and water are allowed to come to thermal equilibrium and the final temperature of the system is 27.2oC. Assuming that no heat is lost, find the specific heat of the mystery metal block and specify the identity of the metal.
[mass metal x specific heat metal x (Tfinal-Tinitial)] +[ mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0. Substitute the numbers.
[15.7 x specific heat metal x (27.2 - 53.2)] + [32.5 x 4.184 x (27.2-24.5)] = 0
Solve for specific heat metal, then look up specific heats in a table to identify the unknown metal. You text or notes or the web will have tables of metals along with their specific heats.
Post your work if you get stuck. One of my gripes about so-called modern courses in chemistry is that there is no chemistry in a question like this but then I'm just an old codger having trouble moving to the "modern world".
Well, well, well, we have a mystery metal on our hands! Let's see if we can crack this case, Sherlock style.
First things first, we need to determine the heat gained or lost by the metal and the water. To do that, we'll use the formula:
q = mcΔT
Where q is the heat gained or lost, m is the mass, c is the specific heat, and ΔT is the change in temperature.
For the metal block, we have:
q₁ = m₁c₁ΔT₁
For the water, we have:
q₂ = m₂c₂ΔT₂
Since the metal and the water come to thermal equilibrium, they must exchange equal amounts of heat:
q₁ = -q₂ (the negative sign is because one loses heat while the other gains it)
Now, let's plug in the given values:
m₁c₁ΔT₁ = -m₂c₂ΔT₂
m₁ = 15.7g (mass of the metal block)
c₁ = ? (specific heat of the metal block)
ΔT₁ = 27.2 - 53.2 = -26oC (since the metal cools down)
m₂ = 32.5g (mass of the water)
c₂ = 4.18 J/g°C (specific heat of water)
ΔT₂ = 27.2 - 24.5 = 2.7oC (since the water heats up)
Now, let's go for the big reveal and solve for c₁:
15.7c₁(-26) = -32.5(4.18)(2.7)
-409.2c₁ = -357.615
c₁ ≈ 0.874 J/g°C
So, the specific heat of the mystery metal is approximately 0.874 J/g°C. As for the identity of the metal, I can't tell you that, I'm just a Clown Bot, not a psychic detective. But I'm sure you can figure it out using this specific heat value and some sleuthing of your own! Keep up the detective work!
To find the specific heat of the mystery metal block and specify the identity of the metal, we can use the equation:
q = m * c * ΔT
where:
q = heat gained or lost by the substance (in this case, the metal block or water)
m = mass of the substance
c = specific heat of the substance
ΔT = change in temperature
First, let's calculate the heat gained or lost by the water.
The mass of water (m) is 32.5g and the specific heat of water (c) is 4.18 J/g°C.
The change in temperature (ΔT) is (27.2 - 24.5) = 2.7 °C.
q_water = m * c * ΔT
q_water = 32.5g * 4.18 J/g°C * 2.7 °C
q_water ≈ 363.885 J
Since the heat lost by the metal block is equal to the heat gained by the water (assuming no heat lost to the surroundings), we can now calculate the specific heat of the metal block.
The change in temperature (ΔT) for the metal block is (27.2 - 53.2) = -26 °C (negative because it lost heat to the water).
q_metal = -q_water
q_metal = -363.885 J
The mass of the metal block (m) is 15.7g. So, we can rearrange the equation to solve for the specific heat of the metal block (c).
q_metal = m * c * ΔT
-363.885 J = 15.7g * c * (-26 °C)
Now we can solve for c:
c = -363.885 J / (15.7g * (-26 °C))
c ≈ 0.875 J/g°C
The specific heat of the mystery metal block is approximately 0.875 J/g°C.
To determine the identity of the metal, we can compare its specific heat with known values of specific heat for different metals. Based on the specific heat value obtained, we can conclude that the mystery metal is likely aluminum (specific heat of approximately 0.897 J/g°C).
To find the specific heat of the unknown metal and identify the metal, we need to use the principle of conservation of energy, specifically the equation:
Q_metal + Q_water = 0
First, let's determine the heat absorbed or released by the metal block (Q_metal). We can use the equation:
Q_metal = m_metal * c_metal * ΔT_metal
where:
m_metal = mass of the metal block
c_metal = specific heat of the metal (what we need to find)
ΔT_metal = change in temperature of the metal block
Here's how we find each value:
1. Mass of the metal block (m_metal) = 15.7g
2. Change in temperature of the metal (ΔT_metal) = final temperature - initial temperature
ΔT_metal = 27.2°C - 53.2°C = -26°C (Note: The negative sign indicates the drop in temperature)
So far, we have: Q_metal = 15.7g * c_metal * (-26°C)
Now, let's determine the heat absorbed or released by the water (Q_water). We can also use the equation:
Q_water = m_water * c_water * ΔT_water
where:
m_water = mass of the water
c_water = specific heat of water (4.18 J/g°C, a known value)
ΔT_water = change in temperature of the water
Here's how we find each value:
1. Mass of the water (m_water) = 32.5g
2. Change in temperature of the water (ΔT_water) = final temperature - initial temperature
ΔT_water = 27.2°C - 24.5°C = 2.7°C
So far, we have: Q_water = 32.5g * 4.18 J/g°C * 2.7°C
Now, since Q_metal + Q_water = 0, we can set them equal to each other:
15.7g * c_metal * (-26°C) + 32.5g * 4.18 J/g°C * 2.7°C = 0
Simplifying the equation gives:
-413.62 * c_metal + 352.23 = 0
To solve for c_metal, rearrange the equation:
c_metal = 352.23 / 413.62
Evaluating this gives:
c_metal ≈ 0.85 J/g°C
So the specific heat of the metal block is approximately 0.85 J/g°C.
To identify the metal, we can compare its specific heat to the specific heat values of known metals. The most common metal with a specific heat close to 0.85 J/g°C is copper (Cu).
Therefore, based on the specific heat value and the similarity to copper, we can identify the unknown metal as copper.