# How to solve this dimensional analysis/stoichometry problem

This problem has been giving me a headache for the last hour on my homework. Does anyone have any pointers in the right direction?

Finally, on January 28th, 2014, in Germany, a barn containing 90 cows exploded when a stray spark caught the methane trapped in the building on fire. Assume that the 90 cows were producing 250 L of methane per day and that there was a 15 hour collection in the barn when it ignited. What mass of water was generated in the explosion?

This problem is specifically about combustion, and I'm assuming I'd have to multiply the combustion equation for methane by 90 somehow. I'm also assuming I'd have to divide 250 / 15 to get the correct liters of methane produced at this time.

• Most of the information is redundant. The key information is 250 L of methane/ 24 h. See how much methane would be there in 15 h. Write an equation on the combustion of methane. What are the products? How many moles of water are generated? – M. Farooq May 7 '20 at 1:50
• This was just the right think I needed to get the gears going. Thank you! – James May 7 '20 at 1:52
• LOL - If ever there was a problem needing reference to a spherical cow then this is it.// Assume 550 kg/cow, that a cow is 70% water, and that the explosion vaporized the cows. – MaxW May 7 '20 at 4:52
• There is no 'correct' answer here as it is, indeed, a combustion problem. As such, per a source, "Methane gas has an LFL of 5.0%. If the atmosphere has less than 5.0% methane, an explosion cannot occur even if a source of ignition is present". The latter implies that 5% or more of the volume of the barn criteria was met. So, depending on the volume of the barn, the answer will decidedly vary! I am also assuming no loss of gas in the sealed barn (also a problematic assumption even given the volume). – AJKOER May 7 '20 at 16:41
• Here is the reference link, for those interested. en.wikipedia.org/wiki/Flammability_limit . Also, the range between Lower and Upper limits is narrow, between 5,0% to 14.3% with a spark, so if the cows produce too much gas per unit volume, the cows are just fine also. – AJKOER May 7 '20 at 16:55

## 1 Answer

Figured it out, thanks to @M. Farooq's help. I first did some cross multiplication of 250/24 times X/15 to find out that in 15 hours, there would be 156.25 L of methane. This is equal to 86.56 grams of methane. Using that, I found out there were 5.393 moles of methane, and multiplying that by 2 (because for every one methane it makes 2 waters) I found that there would be 10.79 mol of water when the reaction was done. This, times the molar mass of water, gives me 194.4 grams of water after the explosion.

• Good job on the problem. – MaxW May 7 '20 at 8:56
• To be precise, I would qualify your answer as 'at most'. A good question in that my comments on LFL, and also of interest is the range between UFL and LFL, may be educational to many. What is especially terrifying is the wide range for H2 (4% to 75%). So, recharging your fuel cell car battery in your garage/house and flipping the light switch in the morning, could be a real bang. – AJKOER May 7 '20 at 17:11