Use the heat equation to calculate the energy, in joules and calo...

Question

Use the heat equation to calculate the energy, in joules and calories, for each of the following (see TABLE3.11):c. lost when 15.0 g of ethanol, C₂H₆O, cools from 60.5 °C to−42.0 °C

Table showing specific heat capacities of methanol in joules and calories per gram per degree Celsius.

Accepted Answer

Welcome back, everyone. We need to determine the heat energy lost in jewels and calories. By using the heat equation. When 35.5 g of a sample of methanol is cooled from 50 degrees Celsius to 25 Celsius. Use the data below. We're given a chart where we have our substance methanol and its associated specific key capacity in jewels per grams times degrees Celsius along with, with its given specific key capacity in Callies per gram times degrees Celsius. Let's begin by recalling our specific heat capacity equation where specific heat capacity represented by the variable C is calculated by taking the heat of our substance Q which is divided by the mass of our substance times the difference in temperature. Delta T recall that our specific heat capacity defines the amount of heat that is needed to change our temperature of one g of our substance by one degree Celsius. So since we need to find the heat that is lost from our cooling of methanol, we're going to want to isolate for Q our term for heat. So we're going to need to multiply both sides by our denominator which consists of mass times the difference in temperature, those terms will cancel on the right. And what we will find is that our heat of our substance methanol is equal to the specific heat capacity multiplied by the mass of our methanol multiplied by the difference in temperature that it undergoes delta T. So let's plug in our nos. But before we do, so, let's calculate our term for delta T which takes the final temperature of our methanol being 25°C. Sorry, that's 25.0 degrees Celsius subtracted from its initial temperature as degrees Celsius. So we have final minus initial And our delta t value is going to equal negative 25°C. So now calculating our heat of methanol will have Q equal to the specific heat capacity of methanol. First in Jews per grams times degrees Celsius as 2.51 Jews divided by grams, times degrees Celsius. This is multiplied by our massive methanol given in our prompt as 35.5 g and multiplied by our delta T which we determined above as negative 25.0 degrees Celsius. Notice that we can cancel our units of Celsius grams and we're left with jewels. So right now we're finding our heat of our methanol in Jews that is lost. And as a result, taking our product, we find our heat of methanol and jewels equal to negative 2227. Jews. Now we're going to round this to three sig figs as negative Jews and notice that this value is negative signaling that heat is lost from ethanol. So this would be our first answer so far. And now we're going to need to calculate our heat of methanol lost in calories. So we're going to plug in our notes beginning with our specific heat capacity of methanol. Now in calories per grams times degrees Celsius. From our chart, we're given a value of 0.600 calories per gram times degrees Celsius. This is then multiplied by our mass of methanol. Again being 35.5 g and multiplied by our delta T which we determined above as negative 25.0 degrees Celsius. So again, canceling out our units of Celsius and grams were left with calories as our final unit. And from our product in our next line, we'll find our heat in calories lost from ethanol's cooling being negative 532.5 calories will round this to a whole number as three sigfig being negative 533 calories. And this would be our second final answer as the amount of heat lost from methanol. So our two final answers would be negative 2230 jews of heat lost from ethanol's cooling as well as five 133 calories of heat lost when Methanol cools. And just to make things clear. We will not include our negative symbol in our final answers because again, the negative symbol just expresses the fact that that amount of heat is lost from our substance methanol. So we will again have 2000, 230 jews of heat lost and 533 calories of heat lost. So I hope that this made sense and let us know if you have any questions.

Use the heat equation to calculate the energy, in joules and calories, for each of the following (see TABLE3.11):c. lost when 15.0 g of ethanol, C₂H₆O, cools from 60.5 °C to−42.0 °C

Key Concepts

Specific Heat Capacity

Heat Equation

Energy Conversion

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