Calculate the specific heat (\rm{J/g \; ^\circ C}) for a 18.5-\rm g sample of tin that absorbs 183 {\rm J} when temperature increases from 35.0 ^\circ \rm C to 78.6 ^\circ \rm C

I can't read most of your post but here is the equation you need.

q = mass x specific heat x delta T.

To calculate the specific heat (\(J/g ^\circ C\)) for a sample of tin, we can use the formula:

\(q = mc\Delta T\),

where:
- \(q\) is the heat absorbed or released by the sample,
- \(m\) is the mass of the sample,
- \(c\) is the specific heat of the substance, and
- \(\Delta T\) is the change in temperature.

In this case, we are given that:
- \(q = 183 J\) (heat absorbed by the tin),
- \(m = 18.5 g\) (mass of the tin),
- \(\Delta T = (78.6 ^\circ C - 35.0 ^\circ C)\) (change in temperature).

Plugging in the given values into the formula, we get:

\(183 J = (18.5 g) \cdot c \cdot (78.6 ^\circ C - 35.0 ^\circ C)\).

Simplifying, we have:

\(183 J = 18.5 g \cdot c \cdot 43.6 ^\circ C\).

To solve for \(c\), we need to rearrange the equation:

\(c = \frac{183 J}{18.5 g \cdot 43.6 ^\circ C}\).

Now, we can calculate the specific heat (\(c\)) for the tin:

\(c = \frac{183 J}{(18.5 g) \cdot 43.6 ^\circ C}\).

Evaluating this expression will give us the specific heat of tin in \(J/g ^\circ C\).