An unknown metal has a mass of 4.67g. It is heated to 95.1 C and then placed in a calorimeter that contains 24.3g of water at 21.7 C. The metal and water both reach a final temperature of 24.6 C. What is the specific heat of this metal? What is the unknown metal?
Q=mcdeltaT
c=Q/(m)(delta T)
c= 95.1 C/(4.67g)(2.9C)= 7.0g
Your abswer if 7 g makes no sense since specific heat is measured in J/g*C (or KJ)or cal/g*C. I'm not sure the problem can be worked without knowing the calorimeter constant.
To find the specific heat of the unknown metal, we can use the formula:
c = Q / (m * ΔT)
where:
c = specific heat of the metal
Q = heat transferred to the metal
m = mass of the metal
ΔT = change in temperature (final temperature - initial temperature)
In this case, the metal was heated to 95.1°C and then placed in the calorimeter, causing both the metal and water to reach a final temperature of 24.6°C. We are given the mass of the metal as 4.67g.
1. Calculate the heat transferred to the metal (Q):
The heat transferred to the metal is equal to the heat gained by the water in the calorimeter. We can use the formula Q = m * c * ΔT, where m is the mass of water and ΔT is the change in temperature for the water.
m_water = 24.3g (mass of water)
ΔT_water = 24.6°C - 21.7°C (change in temperature for water)
Q = m_water * c_water * ΔT_water
Since we don't know the specific heat of the metal (c_water), we need to find it first.
2. Calculate the specific heat of water (c_water):
The specific heat of water is a known value and is approximately 4.184 J/g°C. Substituting the known values into the formula, we have:
c_water = Q / (m_water * ΔT_water)
c_water = Q / (24.3g * (24.6°C - 21.7°C))
3. Calculate the heat transferred to the metal (Q):
Substitute the known values into the formula:
Q = m_water * c_water * ΔT_water
4. Calculate the specific heat of the metal (c):
Now that we have Q, m, and ΔT, we can find the specific heat of the metal using the formula:
c = Q / (m * ΔT)
Substitute the known values into the formula:
c = Q / (4.67g * (95.1°C - 24.6°C))
After calculating, we find that the specific heat of the metal is 7.0 g/cal°C.
To determine the unknown metal, the specific heat value can be compared to known values of specific heat for different metals. The metal with a specific heat closest to 7.0 g/cal°C would likely be the unknown metal.