Question

2hcl + mg → mgcl₂ + h₂
the initial temperature of the 41.3 g of solution is 21.2 °c. the temperature is 76.6 °c at the end of the reaction. what is the heat change for the solution?
c_soln = 4.04 j/g °c
q_soln = m × c × (t_f − t_i)
q_soln = 41.3 × 4.04 × (76.6 − 21.2)
q_soln = ? j
enter either a + or - sign and the magnitude.

Explanation:

Step1: Calculate the temperature change

First, find the difference between the final temperature ($T_f$) and the initial temperature ($T_i$).
$T_f - T_i = 76.6 - 21.2 = 55.4\ ^\circ\text{C}$

Step2: Multiply mass, specific heat, and temperature change

Now, use the formula $q_{\text{soln}} = m \times c \times (T_f - T_i)$. Substitute $m = 41.3\ \text{g}$, $c = 4.04\ \text{J/g}\ ^\circ\text{C}$, and the temperature change we found.
$q_{\text{soln}} = 41.3 \times 4.04 \times 55.4$

First, calculate $41.3 \times 4.04$:
$41.3 \times 4.04 = 166.852$

Then, multiply this result by $55.4$:
$166.852 \times 55.4 = 9243.6008$

Since the temperature of the solution increased (exothermic reaction for the system, but the solution absorbs heat, so $q_{\text{soln}}$ is positive), we use a $+$ sign.

Answer:

$+9240$ (or more precisely $+9243.6$; depending on rounding, but typically rounded to a reasonable number of significant figures. The given values have 3, 3, and 3 significant figures (41.3, 4.04, 55.4), so the answer should have 3 significant figures: $+9240$ J or $+9.24 \times 10^3$ J. If we use the exact calculation: $+9243.6$ J, which can be rounded to $+9240$ J or $+9.24 \times 10^3$ J. However, following the calculation steps precisely: $41.3\times4.04 = 166.852$; $166.852\times55.4 = 9243.6008$, so the answer is $+9240$ J (or $+9244$ J if not rounding intermediate steps).)

(Note: If we do not round intermediate steps, the exact value is approximately $+9243.6$ J, which can be written as $+9240$ J (3 significant figures) or $+9244$ J (more precise).)