Chapter 1: Q45E (page 1)

Consider the substances in Table 9.3. Which substance requires the largest amount of energy to raise the temperature of 25.0 g of the substance from 15.0⁰C to 37.0⁰C? Calculate the energy. Which substance in Table 9.3 has the largest temperature change when 550. g of the substance absorbs 10.7 kJ of energy? Calculate the temperature change.

Short Answer

Expert verified

The amount of energy (heat required) will be 2.3 kJ. The change in temperature will be 139⁰ C.

Step by step solution

Determine the energy required

The amount of heat required to raise one degree Celsius temperature of one gram of substance is known to be the Specific heat capacity. From table 9.3 it can be determined that H₂O(l) have the largest heat capacity value. Therefore, it requires the highest amount of heat for this process.

Given,

$m = m a s s o f t h e e l e m e n t = 25 g C_{p} = H e a t c a p a c i t y = 4.18 \frac{J}{g^{\circ} C} △ T = C h a n g e i n t e m p e r a t u r e = (37^{\circ} C - 15^{\circ} C) = 22^{\circ} C$

The amount of heat required for H₂O(l) is:

localid="1660039497869" $\begin{array}{rcl} Q & = & m C_{p} △ T \\ = & (25 \times 4.18 \times 22) J \\ = & 2299 J \\ \approx & 2.3 k J \end{array}$

Determine the temperature change

The largest temperature change will occur if a certain amount of energy is added to a certain mass of substance with the smallest specific heat capacity. From table 9.3 it can be determined thatHg(l) have the smallest heat capacity value.

Given,

$\begin{array}{rcl} m & = & m a s s o f t h e e l e m e n t = 550 g \\ C_{p} & = & H e a t c a p a c i t y = 0.14 \frac{J}{g^{\circ} C} \\ Q & = & A m o u n t o f h e a t a b s o r b e d = 10.7 k J \end{array}$

Let, $△ T = C h a n g e i n t e m p e r a t u r e$

Therefore, the change in temperature will be

role="math" localid="1660041710659" $△ T = \frac{Q}{m C_{p}} = \frac{10.7 k J \times \frac{1000 J}{k J}}{550 g \times 0.14 \frac{J}{g^{\circ} C}} = 138 . 96^{\circ} C \approx 139^{\circ} C$