An unknown substance has a mass of 16.3 g. The temperature of the substance increases by 20.1 degrees Celsius when 126 J of heat is added to the substance. What is the most likely identity of the substance? The table lists the specific heat capacities of select substances.

Lead 0.128
Silver 0.235
Copper 0.385
Iron 0.449
Aluminum 0.903
Water 4.184

To determine the most likely identity of the substance, we can use the formula:

Q = mcΔT

Where:
Q is the heat absorbed by the substance (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 of the substance (in °C).

Given:
m = 16.3 g
ΔT = 20.1 °C
Q = 126 J

We need to calculate c for each substance and find the one that matches the given data.

For lead:
Q = mcΔT
126 J = 16.3 g * 0.128 J/g°C * 20.1 °C

For silver:
Q = mcΔT
126 J = 16.3 g * 0.235 J/g°C * 20.1 °C

For copper:
Q = mcΔT
126 J = 16.3 g * 0.385 J/g°C * 20.1 °C

For iron:
Q = mcΔT
126 J = 16.3 g * 0.449 J/g°C * 20.1 °C

For aluminum:
Q = mcΔT
126 J = 16.3 g * 0.903 J/g°C * 20.1 °C

For water:
Q = mcΔT
126 J = 16.3 g * 4.184 J/g°C * 20.1 °C

Calculating each of these, we find that none of the substances match the given data exactly. However, the closest match is silver, with a calculated Q value of approximately 123.4 J, which is close to the given value of 126 J. Therefore, the most likely identity of the substance is silver.

q = mass x sp.h. x delta T.

Substitute and solve for specific heat and identify from the table.

Copper

To determine the most likely identity of the substance, we need to calculate its specific heat capacity and compare it with the values given in the table.

The specific heat capacity (C) of a substance is the amount of heat energy required to raise the temperature of 1 gram of the substance by 1 degree Celsius.

The formula to calculate heat energy is given by:

Q = m * C * ΔT

Where:
Q is the heat energy (in joules)
m is the mass of the substance (in grams)
C is the specific heat capacity (in J/g·°C)
ΔT is the change in temperature (in °C)

In this case, we know the mass of the substance (16.3 g), the change in temperature (20.1 °C), and the heat energy (126 J).

We need to rearrange the formula to solve for C:

C = Q / (m * ΔT)

Substituting the given values:

C = 126 J / (16.3 g * 20.1 °C)
C ≈ 0.391 J/g·°C

Now, we can compare this calculated value with the specific heat capacities in the table. The substance with the closest specific heat capacity to 0.391 J/g·°C is Copper (0.385 J/g·°C).

Therefore, the most likely identity of the substance is Copper.