Calculate the amount of energy in kj necessary to convert...

Calculate the amount of energy (in kJ) necessary to convert 497 g of liquid water from 0°C to water vapor at 172°C. The molar heat of vaporization (Hvap) of water is 40.79 kJ/mol. The specific heat for water is 4.184 J/g · °C, and for steam is 1.99 J/g · °C. (Assume that the specific heat values do not change over the range of temperatures in the problem.)

Transcript

00:01 Hi, so we are to calculate the amount of energy or heat required in order to convert the given liquid water to a water vapor at the specified temperature.

00:14 So the temperatures involved are we have initially 0 degrees celsius and this will be heated up to 172 degrees celsius, but at 100 degrees celsius there will be phase change, right, from liquid water to steam.

00:29 So that's liquid to gas.

00:32 Then we have here, final temperature is 172 degrees celsius.

00:37 So from 0 to 100 degrees celsius, there will be change in temperature.

00:42 So that's delta t.

00:44 And then at 100 degrees celsius, there will also be phase change from liquid to gas.

00:53 And then from 100 degrees celsius to 172 degrees celsius, there will be change in temperature again.

01:00 And we'll call the heat required for 0 to 100 degrees celsius temperature change.

01:08 We'll call that q1.

01:09 This will be heat to q2 and this will be q3.

01:13 And then the total heat required for this process qt will be equivalent to q1 plus q2 plus q3.

01:24 Okay.

01:25 And q1 is the heat required for temperature change.

01:31 So this is mass multiplied by the specific heat capacity of liquid water.

01:40 And then multiplied by the change in temperature plus q2, which is heat required for phase change.

01:46 So this will be number of moles multiplied by delta h of vaporization plus q3.

01:53 We now have water vapor so this is the same mass multiplied by the specific heat capacity of steam and then the change in temperature so it's important to take note of the state because the specific heat capacity for liquid water and for steam is different okay so always be mindful of the state so now let's plug in the information that we have mass is 497 grams.

02:30 Specific heat of liquid water is 4 .184.

02:35 This is joules per grams degrees celsius.

02:39 And then the change in temperature, the final temperature is 100 degrees celsius minus the initial temperature for q1, which is 0.

02:48 Okay.

02:49 And then our final answer is in terms of kilojoules.

02:53 So let's just convert joles to kilojoules here.

02:57 1000 joules is one kilojol.

03:01 And then for q2, number of moles, so we need to convert the mass of water to moles.

03:08 4 .97 grams of water divided by the molar mass of water, which is equivalent to 18 .02 grams...