Question

How do you calculate the mass of ethanol that must be burnt to increase the temperature of $210g$ of water by ${65^o}$ , if half of the heat released by this combustion is lost to the surrounding?

Answer 1

It can be calculated by the relation of heat transferred with mass of object. Theoretically, heat transferred is equal to the product of mass of object, specific heat of the object and change in temperature. By using this relation we will get the mass of ethanol.

Formula used:
$q = m{C_S}\Delta T$
Where, $q$ = Heat transferred theoretically
$m$ = mass of object
${C_s}$ = Specific heat capacity of object
$\Delta T$ = Change in temperature

Complete step by step answer:
According to the question:
Mass of water $(m)$ = $210g$
Specific heat capacity of water $({C_s})$ = $4.184J{}^o{C^{ - 1}}{g^{ - 1}}$
Change in temperature $(\Delta T)$ = ${65^o}C$
STEP1: Calculation of heat transferred theoretically
So, we can calculate heat transferred by using the formula given above:
$q = m{C_S}\Delta T$
Where, $q$ = Heat transferred theoretically
$m$ = mass of object
${C_s}$ = Specific heat capacity of object
$\Delta T$ = Change in temperature
By, substituting the values we will get,
$\Rightarrow q = 210g \times 4.184J{}^o{C^{ - 1}}{g^{ - 1}} \times {65^o}C \\\ \Rightarrow q = 57.1kJ \\\$
STEP2: Calculation of actual heat required
Heat required: $\Rightarrow 57.1kJ \times \dfrac{{2kJ}}{{1kJ}}$
$\Rightarrow 114kJ$
STEP3: Calculation of number of moles of ethanol required
The combustion of alcohol follow the reaction given below:
${C_2}{H_5}OH + \dfrac{7}{2}{O_2} \to 2C{O_2} + 3{H_2}O + 1367kJ$
Number of moles required = $114kJ + \dfrac{{1molEthanol}}{{1367kJ}}$
$\Rightarrow 0.0836mol$
STEP4: Calculation of mass of ethanol
Mass of ethanol will be equal to: $0.0836mol \times \dfrac{{46.07gEthanol}}{{1molEthanol}}$
$\Rightarrow 3.8g$
So, the mass of ethanol required is $3.8g$ .

Note:
In Combustion a substance reacts rapidly with oxygen and produces heat. The substance which reacts rapidly with oxygen is called the fuel, and the source of oxygen is called the oxidizer. The fuel can be in the form of a solid, liquid, or gas. For example for airplane propulsion the fuel is usually a liquid. During the process of combustion, the fuel and oxidizer are turned into exhaust products, heat is generated. And also some source of heat is also necessary to start combustion.