A 5.00 g sample of aluminum pellets (specific heat capacity = 0.89 J/°C·g) and a 10.00 g sample of iron pellets (specific heat capacity = 0.45 J/°C·g) are heated to 100.0°C. The mixture of hot iron and aluminum is then dropped into 97.3 g of water at 22.0°C. Calculate the final temperature of the metal and water mixture, assuming no heat loss to the surroundings.

To calculate the final temperature of the metal and water mixture, use the equation q1 + q2 + q3 = 0 and apply the equation q = mcΔT to calculate the heat transferred. Solving for the final temperature will give the result for both the metal and water mixture.

Explanation:

To calculate the final temperature of the system, we can use the equation: q1 + q2 + q3 = 0,

where q1 is the heat transferred from the aluminum pellets to the water,
q2 is the heat transferred from the iron pellets to the water, and
q3 is the heat transferred from the water to the surroundings.

We can calculate q1 and q2 using the equation: q = mcΔT, where q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature. Since the system is completely isolated, q3 is zero.

Using the given values:
For the aluminum pellets: m = 5.00 g, c = 0.89 J/°C·g, ΔT = final temperature - initial temperature.

For the iron pellets: m = 10.00 g, c = 0.45 J/°C·g, ΔT = final temperature - initial temperature.

With these equations, we can solve for the final temperature, which will be the same for both the metal and water mixture.