Baking soda (sodium bicarbonate, NaHCO3) reacts with acids in foods to form carbonic acid 1H2CO32, which in turn decomposes to water and carbon dioxide gas. In a cake batter, the CO21g2 forms bubbles and causes the cake to rise. (c) If 1/2 teaspoon of baking soda is indeed completely neutralized by the lactic acid in sour milk, calculate the volume of carbon dioxide gas that would be produced at 1 atm pressure, in an oven set to 350 F.

Video transcript

All right. Hi, everyone. So this question says that baking soda or sodium bicarbonate and A HCO three reacts with acids in foods to form carbonic acid or H two co three, which in turn decomposes to water and carbon dioxide gas in a cake batter, the carbon dioxide gas forms bubbles and causes the cake to rise. If three quarters of a teaspoon of baking soda is indeed completely neutralized by the lactic acid in 1.5 cup of sour milk. Calculate the volume of carbon dioxide gas that would be produced at one atmosphere of pressure in an oven set to 375 °F. Option A says 2.77 L. Option B says 3.62 L. Option C says 7.24 L and option D says 1.81 L. All right. So first, let's go ahead and write down the balanced chemical reactions for the processes being described. First, we have Lactic acid that's C three cho HC double oh an aqueous solution reacting with the bicarbonate anion that's HCO three negative to form an equilibrium with lactate and carbonic acid. So lactate is the detonated form of lactic acid and carbonic acid is the proton form of carbonate. But in addition to this acid base equilibrium, we also have to consider the decomposition of carbonic acid in which carbonic acid that's H two co three decomposes to form water as a liquid and carbon dioxide gas. So now we can use these balanced chemical equations to solve for the moles of carbon dioxide. But before we do that, let's recall a few different conversion factors that are necessary for this question here, recall it. One cup is equal to 236.6 mL which in turn is equal to 48 teaspoons because notice how the quantity of baking soda is provided in teaspoons. And so by converting units of teaspoons into units of milliliters, we can use the density of sodium bicarbonate to convert volume into mass, right? Because here are given value or our first value is the three quarters teaspoon of baking soda, which is sodium bicarbonate. So first we can go ahead and convert units of teaspoons to units of milliliters using the conversion factor provided. So it's worth mentioning here that the idea is to always cancel out your starting units. So if I'm treating my conversion factor like a fraction, my 48 teaspoons should be in the denominator because this ensures that units of teaspoons cancel out. And so my 236.6 mL should be at the top. So now using the density of sodium bicarbonate, we can go ahead and convert milliliters into grams. Now here recall that the density of sodium bicarbonate is 2.16 g per 1 mL. Once again, milliliters cancel out. And my answer is expressed in units of grams. So now using the molar mass of sodium bicarbonate, we can relate the grams of sodium bicarbonate to the mas because what that does is allow us to then use the stoichiometry coefficients to relate the moles of sodium bicarbonate to the moles of carbon dioxide. So here the molar mass of sodium bicarbonate is 84.01 g per one mole. Notice how grams should be in the denominator to make sure that grams of sodium bicarbonate cancel out. And by denominator, I mean, referring to the conversion factor. All right. So at this point, we have the moles of sodium bicarbonate. But to be a little bit more precise, we want to discuss the moles of bicarbonate specifically because we can then relate that to the moles of carbon dioxide. So my next conversion factor is recalling the fact that one mole of bicarbonate of HC three negative is produced from one mole of sodium bicarbonate because now using our balanced chemical equations here, we can see that one mole of bicarbonate produces one mole of carbonic acid, which then produces one mole of carbon dioxide. So one mole of co two is eventually produced from one mole of HC three negative. So now our task is to evaluate this value right after multiplying all numerators and dividing all denominators, our answer for the moles of carbon dioxide is 0.09505. So now because carbon dioxide is a gas, we can use the ideal gas law to calculate our value according to the conditions provided. So here recall that PV equals NRT. So by rearranging this expression, we get that V is equal to N or T divided by P. But here recall that our temperature was provided in units of Fahrenheit, specifically 375 °F. Now, in the ideal gas law, the temperature must be expressed in units of Calvi. So first, we're going to convert our temperature from degrees Fahrenheit two °C and then we can convert that into Kelvin. So the temperature in Kelvin, I should say is equal to the temperature in degrees Celsius subtracted by or sorry added to 273. Now to convert a temperature from degrees Fahrenheit to degrees Celsius, we're going to take our temperature in degrees Fahrenheit multiply it by nine fifths and then subtract that value by 32. So we can combine those equations to get a final answer in Kelvin or rather slight correction on the formula. My apologies for that to go from degrees Fahrenheit to degrees Celsius. We're going to first take the temperature in degrees Fahrenheit, subtract 32 from that value and then multiply by five overnight just to clarify that. So from here, we can plug in our temperature which was 375 °F subtract 32 from that. And then multiply by five overnight, this is going to give us a temperature in degrees Celsius, which we can then add the 273 to get our final temperature in Kelvin. And after all is said and done, our final temperature equals 463 0.5556 Kelvin. So now we can go ahead and find our volume. So V is equal to N RT divided by P. So N is equal to 0.09505 moles of carbon dioxide multiplied by R which is our gas constant or 0.08 206 liter atmosphere per mole. Kelvin and tea is 463.5556 Kelvin. And so all of this is divided by our pressure which is one atmosphere. So after evaluating our expression, our equation, the volume is equal to 3.6156 L which after rounding to three significant figures, gives us 3.62 L and there you have it. So our final answer or the volume of carbon dioxide gas is 3.62 L. And this matches with option B in the multiple choice. And so if you watch this video, all the way through to the end. Thank you so very much. I appreciate it and I hope you found this helpful.