Question

question 8
two aqueous solutions are mixed in a constant pressure calorimeter to produce a reaction. the calorimeter and solutions are initially at 24.0°c and the final temperature of the system was 31.5°c. if the combined solution gained 1985 j of heat, the combined mass of the aqueous solutions is
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grams. the specific heat capacity is 4.18 j/g.°c. round your answer to three significant figures and do not include units.

Explanation:

Step1: Recall the heat formula

The formula for heat \( q \) is \( q = mc\Delta T \), where \( m \) is mass, \( c \) is specific heat capacity, and \( \Delta T \) is the change in temperature. We need to solve for \( m \), so rearrange the formula to \( m=\frac{q}{c\Delta T} \).

Step2: Calculate the temperature change

The initial temperature \( T_i = 24.0^\circ C \) and the final temperature \( T_f = 31.5^\circ C \). So \( \Delta T=T_f - T_i=31.5 - 24.0 = 7.5^\circ C \).

Step3: Substitute values into the formula

We know \( q = 1985\space J \), \( c = 4.18\space J/g\cdot^\circ C \), and \( \Delta T = 7.5^\circ C \). Substitute into \( m=\frac{q}{c\Delta T} \):

$$ m=\frac{1985}{4.18\times7.5} $$

First, calculate the denominator: \( 4.18\times7.5 = 31.35 \). Then, \( m=\frac{1985}{31.35}\approx63.3 \) (rounded to three significant figures).

Answer:

63.3