Question

when 17.6 g hcl dissociates in 55.0 g of water in a coffee cup calorimeter, the temperature rises from 28.1 °c to 66.5 °c.
\\( c_{sol} = 4.04 j/g °c \\) \\( c_{cal} = 4.90 j/°c \\)
\\( q_{cal} = +188 j \\)
what is the heat of the solution, \\( q_{sol} \\)?
\\( q_{sol} = ? j \\)
enter either a + or - sign and the magnitude.

Explanation:

Step1: Identify the formula for heat of solution

The heat absorbed by the solution (\(q_{\text{sol}}\)) can be calculated using the formula \(q = mc\Delta T\), where \(m\) is the mass of the solution, \(c\) is the specific heat capacity of the solution, and \(\Delta T\) is the change in temperature.
First, find the total mass of the solution: \(m = 17.6\ \text{g} + 55.0\ \text{g} = 72.6\ \text{g}\).
The change in temperature \(\Delta T = 66.5^\circ\text{C} - 28.1^\circ\text{C} = 38.4^\circ\text{C}\).

Step2: Calculate \(q_{\text{sol}}\) using \(q = mc\Delta T\)

Substitute the values into the formula: \(m = 72.6\ \text{g}\), \(c = 4.04\ \text{J/g}^\circ\text{C}\), \(\Delta T = 38.4^\circ\text{C}\).
\(q_{\text{sol}} = 72.6\ \text{g} \times 4.04\ \text{J/g}^\circ\text{C} \times 38.4^\circ\text{C}\)
First, calculate \(72.6 \times 4.04\): \(72.6\times4.04 = 293.304\)
Then, multiply by \(38.4\): \(293.304\times38.4 = 11262.8736\)
Since the temperature of the solution rises, the solution absorbs heat, so \(q_{\text{sol}}\) is positive.

Answer:

\(+11263\) (rounded to a reasonable number of significant figures, or keeping the precise value as \(+11262.8736\) which can be rounded to \(+11263\))