a 225.0 g sample of an unknown, silver, pure metal was heated to 95.5 degrees celsius then put into 150.50 g of water at 22.5 degrees celsius. the water was heated by the hot metal to a temperature of 31.4 degrees celsius. what is the specific heat? what is the metal?
metal loss of heat + water gain of heat = 0
[(mass metal x specific heat metal x (Tfinal-Tinitial)] + [mass H2O x specific heat H2O x (Tfinal-Tinitial)] = 0
Substitute the numbers and solve for specific heat metal. Then look up in a specific heat table to identify the metal.
To find the specific heat of the metal and determine its identity, we need to use the equation:
q = m × c × ΔT
where:
q = heat gained or lost by the system
m = mass of the substance
c = specific heat capacity of the substance
ΔT = change in temperature
First, let's find the heat gained or lost by the water using the equation:
q_water = m_water × c_water × ΔT_water
Given:
m_water = 150.50 g (mass of water)
c_water = 4.18 J/g·°C (specific heat capacity of water)
ΔT_water = T_final - T_initial = 31.4°C - 22.5°C = 8.9°C (change in water temperature)
Substituting the given values into the equation, we can calculate q_water:
q_water = 150.50 g × 4.18 J/g·°C × 8.9°C
Solving this equation gives us the value of q_water.
Now, let's find the heat gained or lost by the metal using the equation:
q_metal = m_metal × c_metal × ΔT_metal
Given:
m_metal = 225.0 g (mass of metal)
c_metal = ? (specific heat capacity of the metal)
ΔT_metal = T_final - T_initial = 31.4°C - 95.5°C = -64.1°C (change in metal temperature)
Since the metal is losing heat to the water, the change in temperature is negative. Substituting the given values into the equation, we have:
q_metal = 225.0 g × c_metal × -64.1°C
Now, we know that the heat gained by the water is equal to the heat lost by the metal (assuming no heat loss to the surroundings):
q_water = q_metal
Therefore, we can set up an equation equating the two:
150.50 g × 4.18 J/g·°C × 8.9°C = 225.0 g × c_metal × -64.1°C
Simplifying and solving for c_metal will give us the specific heat capacity of the metal.
Once we find the specific heat capacity of the metal, we can use reference tables or periodic tables to identify the metal based on its specific heat capacity.