help with this problem pease
Metal Specific Heat (J/g-C)
Al (s) 0.900
Au(s) 0.129
Cu(s) 0.385
Fe(s) 0.444
Hg(l) 0.139
H2O(l) 4.184
C2H5OH(l) 2.46
A piece of metal at a temp of 101.0oC and a mass of 86.0 g is dropped into a beaker of water containing 75.0 ml at a temp. of 27.0oC. If the final temperature reached is 35.0oC, what is the identity of the metal?
the sum of the heats gained is zero.
heatgainedmetal+heatgainedwater=0
86*cm*(35-101)+75*cw(35-27)=0
solve for cm.
To determine the identity of the metal, we can use the principle of heat transfer. We know that heat gained by the water is equal to the heat lost by the metal.
The formula for heat transfer is Q = m * c * ΔT, where Q represents the heat transferred, m is the mass, c is the specific heat, and ΔT is the change in temperature.
First, calculate the heat gained by the water:
Q_water = m_water * c_water * ΔT_water
Given that the mass of water is 75.0 g (assuming density of water = 1 g/ml), the specific heat of water is 4.184 J/g-C, and the change in temperature is 35.0oC - 27.0oC = 8.0oC.
Q_water = 75.0 g * 4.184 J/g-C * 8.0oC
Next, calculate the heat lost by the metal:
Q_metal = m_metal * c_metal * ΔT_metal
Given that the mass of the metal is 86.0 g and the initial temperature of the metal is 101.0oC, we need to determine the ΔT_metal (change in temperature of the metal).
ΔT_metal = Final temperature - Initial temperature = 35.0oC - 101.0oC = -66.0oC (negative because heat is lost)
Now, we can calculate the heat lost by the metal using the given specific heat values:
Q_metal = 86.0 g * c_metal * -66.0oC
To find the identity of the metal, we need to compare the amount of heat gained by the water (Q_water) and the amount of heat lost by the metal (Q_metal). The specific heat value for the metal that matches the calculated heat transfer value will be the identity of the metal.
Compare Q_water and Q_metal:
Q_water = Q_metal
75.0 g * 4.184 J/g-C * 8.0oC = 86.0 g * c_metal * -66.0oC
Simplify the equation:
(c_metal * -66.0oC) = (75.0 g * 4.184 J/g-C * 8.0oC) / 86.0 g
Now, plug in the known values and solve for c_metal:
c_metal = [(75.0 * 4.184 * 8.0) / 86.0] / (-66.0)
Calculating:
c_metal = -0.385 J/g-C
Comparing this specific heat value with the metal specific heat values provided, we find that it matches the specific heat value for copper (Cu).
So, the identity of the metal is copper (Cu).