Question

first calculate the heat required to increase the temperature of 25.0 g solid ethanol (c₂h₅oh) from -135°c to its melting point temperature of -114°c. (give the answer in j.)
q = j
now calculate the heat required to melt 25.0 g of ethanol at -114°c. (give the answer in kj.)
q = kj
calculate the amount of heat needed to raise the temperature of the 25.0 g liquid ethanol from its melting point of -114°c to 72°c. (give the answer in j.)
q = j
calculate the total heat in kj required to raise the temperature of 25.0 g of solid ethanol at -135.0°c to liquid at 72.0°c. (give the final answer in kj.)
q = kj

Explanation:

Step1: Calculate heat for temperature increase of solid ethanol

The formula for heat \( q = mc\Delta T\). For solid ethanol, \(c = 0.97\space J/g^{\circ}C\), \(m = 25.0\space g\), \(\Delta T=T_{final}-T_{initial}=- 114^{\circ}C-(-135^{\circ}C)=21^{\circ}C\)

$$q_1 = 25.0\times0.97\times21$$

$$q_1=25.0\times20.37 = 509.25\space J$$

Step2: Calculate heat for melting of ethanol

The heat of fusion of ethanol \( \Delta H_{fus}=109\space J/g\). Using \(q = m\Delta H_{fus}\), with \(m = 25.0\space g\)

$$q_2=25.0\times109 = 2725\space J=2.725\space kJ$$

Step3: Calculate heat for temperature increase of liquid ethanol

For liquid ethanol, \(c = 2.3\space J/g^{\circ}C\), \(m = 25.0\space g\), \(\Delta T=72^{\circ}C-(-114^{\circ}C)=186^{\circ}C\)

$$q_3 = 25.0\times2.3\times186$$

$$q_3=25.0\times427.8=10695\space J$$

Step4: Calculate total heat

First convert \(q_1 = 509.25\space J = 0.50925\space kJ\) and \(q_3 = 10695\space J=10.695\space kJ\)

$$q_{total}=q_1 + q_2+q_3$$

$$q_{total}=0.50925 + 2.725+10.695$$

$$q_{total}=13.92925\approx13.9\space kJ$$

Answer:

\(q_1 = 509\space J\)
\(q_2 = 2.725\space kJ\)
\(q_3 = 10695\space J\)
\(q_{total}=13.9\space kJ\)