Question

An 80.0 g sample of metal, initially at 96.0 °C, is placed into 150.0 g of water initially at 26.0 °C in a calorimeter. The final temperature of the water is 28.1 °C. What is the identity of the metal?

Answer 1

To determine the specific heat and identity of the metal, you can use the equation
`q_{metal` +
`q_{water` = 0. Calculate
`q_{metal` and
`q_{water` using the formulas
`q_{metal` =
`m_{metal` *
`c_{metal` * (
`T_(metal)_{final`-
`T_(metal)_{initial`) and
`q_{water` =
`m_{water` *
`c_{water`* (
`T_(water)_{final`-
`T_(water)_{initial`). Compare the calculated specific heat of the metal to known specific heats to determine its identity.

To determine the specific heat and identity of the metal, we can use the equation:

`q_{metal` +
`q_{water` = 0

where
`q_{metal` is the heat gained or lost by the metal and
`q_{water` is the heat gained or lost by the water. We can calculate
`q_{metal` using the formula:

`q_{metal` =
`m_{metal` *
`c_{metal` * (
`T_(metal)_{final` -
`T_(metal)_{initial`)

where
`m_{metal` is the mass of the metal,
`c_{metal` is the specific heat of the metal,
`T_(metal)_{final` is the final temperature of the metal, and
`T_(metal)_{initial` is the initial temperature of the metal. Similarly, we can calculate
`q_{water`using the formula:

`q_{water` =
`m_{water` *
`c_{water` * (
`T_(water)_{final` -
`T_(water)_{initial`)

where
`m_{water` is the mass of the water,
`c_{water` is the specific heat of water,
`T_(water)_{final` is the final temperature of the water, and
`T_(water)_{initial` is the initial temperature of the water.

Plugging in the given values:

`m_{metal`= 92.9 g

`T_(metal)_{initial` = 178.0 °C

`T_(metal)_{final` = 29.7 °C

`m_{water`= 75.0 mL = 75.0 g

`T_(water)_{initial` = 24.0 °C

`T_(water)_{final` = 29.7 °C

`c_{water` = 4.18 J/g·°C

Solving the equations, we find that
`c_{metal` = 0.94 J/g·°C.

To confidently determine the identity of the metal, we can compare the calculated specific heat of the metal (0.94 J/g·°C) to the known specific heat of different metals. The metal with the closest specific heat to 0.94 J/g·°C is most likely the identity of the metal.