Question

A 2.45 g sample of a substance suspected of being pure gold is warmed to 72.2 ∘c and submerged into 15.4 g of water initially at 24.3 ∘c . the final temperature of the mixture is 26.9 ∘c .

Answer 1

Using the principles of calorimetry and specific heat capacities, the heat absorbed by the gold sample can be calculated. The final temperature of the mixture suggests that heat was transferred from the gold to the water, allowing determination of the specific heat capacity of gold.

Step-by-step explanation:

To determine the heat absorbed by the gold sample, we can use the principle of calorimetry. The heat lost by the gold
`(Q_lost)` is equal to the heat gained by the water
`(Q_gained)` according to the formula
`\( Q = mc`ΔT , where Q represents heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

Firstly, calculate the heat absorbed by the water using the formula
`\( Q_(water)` =
`m_(water)c_(water)`ΔT
`_(water) \)`, where
`\( m_(water) \)` is the mass of water,
`\( c_(water) \)` is the specific heat capacity of water, and ΔT
`_(water) \)` is the change in temperature of water.

Next, equate the heat lost by the gold to the heat gained by the water:
`\( Q_(gold) = -Q_(water) \)`. Rearrange the equation to find the specific heat capacity of gold
`(\( c_(gold) \))` using the mass of the gold sample, the temperature change of the gold, and the calculated heat exchange.

By rearranging the formula Q = mcΔT, you can isolate the specific heat capacity c to find the value for gold. This calculation allows us to determine the specific heat capacity of the substance suspected to be pure gold.