a 5.00 gram sample of a metal is heated to 80 degrees Celsius and is placed in a 100 gram sample of water. the temperature of the water rises from 20 Celsius to 20.3 Celsius which of these is most likely to be the metal
You didn't list any choices but here is how you work the problem
heat lost by metal + heat gained by water = 0
[mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute and solve for specific heat of the metal. Compare specific heats to determine the identify of the metal.
To determine which metal is most likely present in the mixture, we can calculate the specific heat capacity of each potential metal and compare it to the observed temperature change.
The equation for calculating the quantity of heat transferred (Q) is:
Q = m * c * ΔT
where:
Q is the heat transferred (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in J/g°C), and
ΔT is the change in temperature (in °C).
The heat transferred by the metal can be calculated using the given information:
Q_metal = m_metal * c_metal * ΔT_metal
Similarly, the heat transferred by water can be calculated:
Q_water = m_water * c_water * ΔT_water
Since the heat gained by the water is equal to the heat lost by the metal (in a closed system with no heat loss to the surroundings), we can equate the two expressions:
Q_metal = Q_water
m_metal * c_metal * ΔT_metal = m_water * c_water * ΔT_water
Rearranging the equation to solve for the specific heat capacity of the metal (c_metal):
c_metal = (m_water * c_water * ΔT_water) / (m_metal * ΔT_metal)
Now, we need to calculate the value of c_metal using the given values:
m_metal = 5.00 grams (mass of the metal)
ΔT_metal = (80°C - 20°C) = 60°C (change in temperature of the metal)
m_water = 100 grams (mass of water)
ΔT_water = (20.3°C - 20°C) = 0.3°C (change in temperature of the water)
Assuming the specific heat capacity of water is approximately 4.18 J/g°C, we can substitute the values into the equation:
c_metal = (100 g * 4.18 J/g°C * 0.3°C) / (5.00 g * 60°C)
Calculating the expression gives us the specific heat capacity of the metal (c_metal).
By comparing the calculated value of c_metal with established values for specific heat capacities of different metals, we can determine which metal is most likely present.