Sulfur burns to SO2 with a beautiful deep blue-purple flame,...

Sulfur burns to $\mathrm{SO}_{2}$ with a beautiful deep blue-purple flame, but with a foul, suffocating odor: $2 \mathrm{S}+\mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{2}$. (a) How many liters of $\mathrm{O}_{2}$ are needed to form $35.2 \mathrm{L} \mathrm{SO}_{2}$, both gases being measured at 741 torr and $26^{\circ} \mathrm{C} ?$ (b) What if only the $\mathrm{SO}_{2}$ is at those conditions, but the $\mathrm{O}_{2}$ is at $17^{\circ} \mathrm{C}$ and 847 torr?

Key Concepts

Stoichiometry

Stoichiometry involves using the balanced chemical equation to determine the mole-to-mole relationships between reactants and products. In this context, the reaction 2S + O2 ? 2SO2 shows that 1 mole of O? produces 2 moles of SO?. This relationship is essential for calculating the amount of one gas required based on the given amount of another, converting volumes or moles as needed.

Ideal Gas Law

The ideal gas law (PV = nRT) relates the pressure, volume, temperature, and number of moles of a gas. It provides a way to calculate the volume of a gas under given conditions or to convert between gas volumes measured at different temperatures and pressures. This concept is key when working with gases that are not all measured at standard conditions, allowing for adjustment of the different states of reactants or products.

Pressure and Temperature Unit Conversions

Accurate gas calculations require converting pressure and temperature measurements to appropriate units, such as converting torr to atmospheres or Celsius to Kelvin. This standardization is crucial when applying the ideal gas law, ensuring that all variables are expressed in compatible units, thereby allowing for correct computation of volumes, moles, or pressures.

Transcript

00:01 Hi there, i am going to begin this problem by writing out the balanced equation that was given in the problem.

00:08 That is two sulfur reacts with oxygen gas to produce two volumes of sulfur dioxide gas.

00:28 And we are given 35 .2 liters as the amount of sulfur dioxide that we want to produce.

00:40 The question asks us how many liters of oxygen we would need to start with to produce this much sulfur dioxide.

00:51 There's actually two problems here.

00:54 In the first problem, letter a, it says that we can assume that the temperature and pressure of these gases is the same.

01:03 Well, if that's the case, then the ratio given to us in the balanced equation can be our volume ratio.

01:11 And we can do this in one step because any gas at the same temperature and pressure will occupy the same volume when you have the same number of moles.

01:24 So for part a, i can simply start with my 35 .2 liters of s .o2, and i can look at the balanced equation for the volume ratio.

01:42 For every two liters of s .o .2, i would need to start with one liter of o2.

01:52 My leaders of s -o -2 cancel.

01:55 Doing my math, i find that i would need to start out with 17 .6 liters of o2.

02:02 Part b is a little bit more complex, however, because the oxygen and the sulfur dioxide are not at the same temperature and pressure.

02:12 The sulfur dioxide is at 26 degrees celsius and 741 tor, while the oxygen is at 7 .4.

02:29 Degrees celsius and 847 tor.

02:40 I'm going to go ahead and change my celsius temperatures to kelvin right away by adding 273.

02:48 So that gives me 290 kelvin for that set of variables.

02:57 And if i add 273 to 26 celsius, i get 299 kelvin for this one.

03:08 All right, these two gases are under two different sets of conditions.

03:14 In order to do my stuichiometry, they need to be under the same conditions.

03:21 So what i want to do is adjust my initial volume of so2 to the volume that it would have if it were under the conditions of the oxygen.

03:32 That means i have a volume, a temperature, and a pressure, and i'm trying to change it to the new volume at the new temperature and pressure.

03:39 It sounds like a combined gas law problem where i'm going to need to use p1 v1 over t1 equals p2 v2 over t2 to determine how many liters of sulfur dioxide i would be starting with under the conditions of the oxygen.

04:04 So i want to get them both under the same set of conditions...

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