Hydrogen gas (a potential future fuel) can be formed by the react...

Question

Hydrogen gas (a potential future fuel) can be formed by the reaction
of methane with water according to the equation:
CH4( g) + H2O( g)¡CO( g) + 3 H2( g)
In a particular reaction, 25.5 L of methane gas (measured at a
pressure of 732 torr and a temperature of 25 °C) mixes with
22.8 L of water vapor (measured at a pressure of 702 torr and a
temperature of 125 °C). The reaction produces 26.2 L of hydrogen
gas at STP. What is the percent yield of the reaction?

Accepted Answer

Hi everyone here we have a question that tells us the reaction between nitrogen dioxide and hydrogen gas produces ammonia and water as a gas. And our reaction is to nitrogen dioxide gasses plus seven hydrogen gasses forms to ammonia gasses plus four water gasses. And it tells us that in a particular reaction nitrogen dioxide gasses at 23.1 liters 783 Tour and 68.0 degrees Celsius was mixed with hydrogen gas, 24.8 liter 731 Tour and 75.0 degrees Celsius, which produced 4.67 liters of ammonia at gas at standard temperature and pressure. And our goal here is to calculate the percent yield of this reaction. So we're going to use the formula P. V. Equals N. R. T. And first we're going to solve for our moles. So to do that, we're going to divide both sides by our R. T. And that gives us number of moles equals pressure times volume over r gas constant times our temperature. So we're gonna start solving for our nitrogen dioxide gas. So our volume equals 0.1 leaders. Our pressure Equals 783 tours and we want to change that to atmosphere. So we're going to multiply by one atmosphere Divided by 760 tour And our tour is going to cancel out leaving us with 1.03 atmospheres and our temperature Equals 68.0°C. And we want that in Kelvin. So we're going to add 273.15. And that equals .15 Kelvin. So now we can solve for the number of moles. So in is going to equal one .03, atmospheres Times 23.1 L, divided by 0.08, Times .15 Kelvin. And that equals zero 8502 moles. And now we're going to solve for our hydrogen gas. Our volume equals 24.8 L. Our pressure equals 731 tour and we want that in atmosphere. So we're gonna times by one atmosphere Over 760 tour And our tours are going to cancel out. And that is going to equal 0. atmospheres. And our temperature is going to equal 75.0° C. And we're going to add 273.15 to change it to Kelvin and that equals 348.15 Kelvin. And now we can solve for the number of moles. So N is going to equal 0. atmospheres Times 24.8 l over 0.08 - 06, which is our gas constant times 348.15 Kelvin. And that is going to equal 0. moles. So because we have less moles of hydrogen hydrogen is our limiting reactant. So now we can calculate our theoretical yield So 0.8349 moles of hydrogen Times are multiple ratio. Which we get from our balanced equation which was given to us in the prompt. So times two moles of ammonia over seven moles of hydrogen Equals 0.2385 moles of ammonia. So that's how much we should get theoretically. So now we're gonna go back to our formula PV equals N. R. T. And this time we're gonna solve for volume. So to do that we're just gonna divide both sides by pressure. So we're going to get volume equals number of moles times r gas constant times temperature divided by pressure. So our volume is going to equal 0.2385 moles of ammonia Times 0.08206 Times 273 .15 Kelvin over one atmosphere because we are at standard temperature and pressure and that equals 5. 59 liters. And now that we have that we can calculate our percent yield, our formula for percent yield is percent yield equals actual yield over theoretical yield times 100. So our percent yield Equals 4.67 l Over 5.3459 l times And that equals 87.4%. And that is our final answer. Thank you for watching. Bye

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