A gaseous hydrogen- and carbon-containing compound is decomposed
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Question

A gaseous hydrogen- and carbon-containing compound is decomposed
and found to contain 82.66% carbon and 17.34% hydrogen
by mass. The mass of 158 mL of the gas, measured at 556
mmHg and 25 °C, was 0.275 g. What is the molecular formula
of the compound?

Accepted Answer

Welcome back everyone in this example, we have a gaseous hydrocarbon with 79.85% carbon and 20.15% hydrogen by mass. So we're told at the pressure of 760 millimeters of mercury and the temperature 25 degrees Celsius. We have a 256 millimeter sample of the gas measured to have a mass of 2560.315 g. And we need to identify the molecular formula of the compound. So we want to recall that our molecular formula is going to tell us the quantity of each element in our compound. And in order to get to this value, we're going to need to recall our ideal gas law, which we should recall is pressure times volume equal to the molds of our gas, end times the gas constant r times the temperature in kelvin. And so we want to go ahead and recall that our molds of our gas can also be understood as the moles or sorry, the mass of our gas divided by our molar mass of our compound. And so instead of saying massive gas in the numerator, we can just say the mass of our gas sample to be specific. So what we want to do now that we understand this is to say that therefore we can say that our ideal gas law can be written as pressure times volume set equal to the mass of our gas times the gas constant r times temperature and then divided by our molar mass. And so as we stated, we want to solve for molar mass in order to get to our molecular formula. So we would say that molar mass is equal to our mass of our gas sample times the gas constant R times temperature divided by our pressure times our volume. Let's make this fraction line better. So let's plug in what we know from our prompt. So according to the prompt, we have a sample that is .315g. So we'll use the color red for the mass of our sample. Here We plug in 0.315g. And then we have our gas constant R. Which we should recall is equal to a value of 0.8206 leaders times a T. M's divided by moles times Calvin. And then we have to plug in our temperature and we'll use the color purple for temperature. So according to the prompt, we have a temperature of 25°C but we should recall that temperature should be in units of Kelvin. And so we're going to say that 25 degrees Celsius plus 73.15 is equal to 2 98. kelvin. And so we can plug that in as our temperature value. And so in our denominator, now that we've completed our numerator, we're going to plug in our values. So we have our pressure and we'll plug in the color black for pressure. So we have for pressure according to the prompt value of 760 millimeters of mercury. But we should recognize that because we have units of a tM in r. Gas constant R. We want to convert from millimeters of mercury to a t. M. And so we're going to recall the conversion factor that for 760 millimeters of mercury that is equivalent to 1 80 M. This allows us to cancel out millimeters of mercury leaving us with a T. M. Units. And then we have our volume which will just also plug in the color black And according to the prompt, that volume is 256 ml. So we'll just actually parentheses here. So we have 256 ml. But we should recognize also that in r gas constant. We used units of leaders. And so we're going to convert from are prefixed middle leaders to the base unit leaders, which tells us that we have 10 to the negative third leaders in one middle leader. And so now we're able to cancel our units of middle leaders and we're left with leaders. And so now we can go ahead and focus on canceling our units in our entire quotient. So canceling out these units. We can go ahead and get rid of leaders now that we have leaders in the denominator. We can also get rid of a T. M's because it's also in the denominator and we can get rid of kelvin here with kelvin here. And this is going to leave us with grams per mole. And sorry about that. So we have grams per mole as our final unit here. And that is the correct final unit for molar mass. So now we can plug in this entire quotient into our calculators and we're going to get a value equal to 30.1 g per mole as our molar mass of our compound. And so this is going to be helpful to us because as we calculate for our molecular formula, we're going to refer to the percent by mass values given for each of our compounds or our elements, sorry, in our compound to get our molecular formula. And so beginning with the first element being carbon here. So for carbon, according to the prompt For our 30.1 g per mole compound that we just solved for above we have a percent by mass, which we will multiply as a conversion factor, which tells us according to probably have 79. g of carbon. And this is a percentage or percent by mass value. So this is out of 100 g of carbon. So we are able to get rid of one of our units of grams. Leaving us with still grams per mole. But next we want to go ahead and recall from our periodic tables our molar mass of carbon. And so this is going to give us according to the periodic table 12. g of carbon. And this is for one mole of carbon since we have a molar mass value, I'm sorry, that's just a C there. So let's go ahead and correct that. So now we can go ahead and get rid of grams. And we're left with are units of just moles here. And so in our calculators, this quotient is going to give us a value that is equal to two moles of carbon. So we get a value of 2.00, which we can round 22. And this is Permal of our compound of our gas compound. So now that we have that value, let's continue on. And we're listed our second element in our hydrocarbon, which is hydrogen here. So we're given its percent by mass And this is according to our molar mass of our gaseous hydrocarbon as calculated above as 30.1 g per mole. We're going to multiply by the% 20. g of hydrogen out of 100 g total. Since it's a percentage this allows us to get rid of grams so far and now we are left with still grams per mole, which we will use as a conversion factor the molar mass of hydrogen from the periodic table, which we see as a value of 1.1 g of hydrogen for one mole of hydrogen. And now we are able to get rid of grams. We want to keep our units of moles here. And so what we're going to get here is a value equal to, we can say about six moles of hydrogen and this is per mole of our gas compound. And so because we have these values here, we can say that therefore our molecular formula, since we know the quantity of each element is going to be c two H six. And so for our final answer, this will correspond to choice B. So what's highlighted in yellow here is going to be our final answer to complete this example. So I hope that everything that I reviewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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