(b) Assuming that there is an uncertainty of 0.002 °C in each temperature reading and that the masses of samples are measured to 0.001 g, what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

Question

Accepted Answer

hi everyone for this problem, we're given the following information and we're being asked to calculate the uncertainty in the calculated value of the molar heat of combustion of fennel. If there is an uncertainty of points 001°C in each temperature reading and .001g for the mass of the samples. Okay, so our goal here for this problem is to calculate the uncertainty okay in the calculated value of the molar heat of combustion. So that means our final answer is going to be in kila jewels. And what we want to do here is because we're given values. The overall uncertainty is approximately equal to the sum of the uncertainties due to each effect. So, we have a couple of effects here in this problem that we need to take note of. Okay, so we have to value line, we have fennel. We're told the mass of the samples for both. Okay. And we're told the temperatures Okay. And at the bottom we're told that There is an uncertainty of .001°C in each temperature reading and .001g for each mass of the samples. So let's go ahead and write out what we're starting with which is what is given. We're told that we have 3000 and 58 killer jewels Permal. Okay, so starting there, that's what we're going to start with and we're going to take the some of the uncertainties due to each effect. Okay, so let's go ahead and get started. We're going to multiply this by the sum. So our first sample is towline. So we know we have 0.531 g sample of towline and the uncertainty at the bottom we're told is 0.1 g. Okay, so we're going to take 0.0 g. That uncertainty and divided by our mass of towline which is 10.531 g. Okay, so I'll write this in a different color that this is tall. You lean. Okay, next we have our fennel. Okay, so our uncertainty is 0.001g. And the mass of our towline or our sample is 0.4-5g. Okay, so now we're going to take into account the temperature uncertainty. Okay, so for our Tall you line, we're told that our uncertainty is 0.001°C. And the temperature we're told is 2.635°C. So we're right tall you line. and for Fennel We're told the uncertainty is zero 0.1°C and the temperature is one .613°C. Okay, so this is us taking the The some of the uncertainties due to each effect and multiplying it by what we're starting with. Okay, so when we do this calculation, we're going to get 16 killer jules. Okay. And this is the uncertainty the calculated uncertainty value of the molar heat of combustion. Okay, so this is going to be our final answer here and that is the end of this problem. I hope this was helpful.

(b) Assuming that there is an uncertainty of 0.002 °C in each temperature reading and that the masses of samples are measured to 0.001 g, what is the estimated uncertainty in the value calculated for the heat of combustion per mole of caffeine?

Verified Solution

Key Concepts

Uncertainty in Measurements

Heat of Combustion

Propagation of Uncertainty