A calorimeter contains 39.1 g of water at 22.0°C. When a sample of silver at 100°C was placed in it, the final temperature was 27.0°C. Determine the mass of the silver sample.

Question

High School

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Answer :

ishika20sam ishika20sam · Answer 1 · 2024-05-20T11:08:36-04:00

The mass of the silver sample is approximately 39.9 grams.

m_silver = (39.1 × 4.18 × (27.0 - 22.0)) / (0.235 × (27.0 - 100))

m_silver ≈ 39.9g

To determine the mass of the silver sample, we can use the principle of heat transfer and the specific heat capacity equation.

First, we need to calculate the heat lost by the silver and gained by the water using the equation:

Q (heat lost by silver) = Q (heat gained by water)

The formula for calculating heat is:

Q = m × c × ΔT

Where Q is the heat, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

The specific heat capacity of water is approximately 4.18 J/g°C, and for silver, it is 0.235 J/g°C.

The initial temperature of the water is 22.0°C, the final temperature is 27.0°C, and the mass of water is 39.1g.

Using the equation, we have:

(m_silver × c_silver × ΔT_silver) = (m_water × c_water × ΔT_water)(m_silver × 0.235 × (27.0 - 100)) = (39.1 × 4.18 × (27.0 - 22.0))

Solving this equation, we find:

m_silver = (39.1 × 4.18 × (27.0 - 22.0)) / (0.235 × (27.0 - 100))

m_silver ≈ 39.9g

Therefore, the mass of the silver sample is approximately 39.9 grams.

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