Under constant-volume conditions, the heat of combustion of benzoic acid (C₆H₅O₆) is 15.57 kJ/g. A 3.500-g sample of sucrose is burned in a bomb calorimeter. The temperature of the calorimeter increases from 20.94 to 24.72 °C. (b) If the size of the sucrose sample had been exactly twice as large, what would the temperature change of the calorimeter have been?

Video transcript

Hi everyone. See we have a 3.5 g sample of repose. It's burned in a bond calorie emitter. The temperature increases from 20.3, 30.5° C calculate the total heat capacity of the caliber ammeter. Given that the heat of combustion of ribose, He's making a 15.62 killer jules program. And we're also as calculate the temperature change. The path of the initial sample of repose was used. So for this we're gonna have negative heat of the reaction equal to the heat of the calorie emitter. The negative part of the reaction is negative mass. How's the entropy of the reaction in the heat of the calorie meter? The total key capacity of the calorie emitter. How's the temperature change The mask? You have 3.5 France for the heat of combustion? -15.62 Hello jules program for the total capacity of the calendar emitter. This is what we're looking for And for the temperature change 30.5 very Celsius -20. degree Celsius Give us 10.2 very Celsius. So now if we plug our bodies into the equation we're gonna get negative 3. gramps That was negative 15.62 little jewels Program Siegel said the total capacity of the calorie meter. I'm 10.2 very Celsius. Sophie divide both sides by 10.2°C. The total capacity of the calorie meter Gonna be 5.36. Hello jules four degrees Celsius. Now to consider the temperature change, we're gonna consider the pleasure negative mass times the entropy other reaction. Because the total capacity of the calorie meter, how's the temperature change? So the entropy of the reaction and the total capacity of the calorie emitter are constant. So we can cancel these out. So this means that the mass is going to be directly proportional to the temperature change. So this means that half of the mass used will give half of the temperature change 10.2°C. About two. We're going to get 5.1 degrees Celsius. Thanks for watching my video and I hope it was helpful.