13.74 l of hydrogen gas at 30 degrees c and 801 torr and 6.55 l of oxygen gas at 25 degree c and 801 torr are drawn into a cylinder where the following reaction takes place. 2 h2 (g) + o2 (g) -> 2h2o (l) what is the limiting reactant? if 8.7 g of water are produced what is the percent yield?

We have an ideal gas equation PV = nRT => n = (PV)/RT 
R = Ideal Gas constant = 0.082
 T, temparature of hydroxen = 30 + 273.15 = 303.15K
 Temperature of oxygen = 25 + 273.15 = 298.15
 P, pressure is 801 torr for both oxygen and hydrogen, 801torr = 801mmHg 
 1 atm = 760mmHg => 801 torr = 1.054atm.
 1): For Hydrogen 13.74 L volume => 
 n = (1.054*13.74)/(0.082*303.15) = 0.582mol
 For Oxygen 6.55 L volume => 
 n = (1.054*6.55)/(0.082*298.15) = 0.282mol
 From equation there is 0.282mol of oxygen which is equal to the calculated
making it a limiting reactant whereas there is 0.291mol of hydrogen from
equation which is less than the calculated.
 Hence deducing that oxygen is the limiting reactant as it has very few moles.
 2): Calculating the yield of water with the help of stoichiometry principles and moles of oxygen, 
  = 0.282mol x (2molH2O/1molO2)*(18gH2O/1molH2O) = 36 x 0.282 g H2O
= 10.15gH2O
 Produced yield is 8.7 g of water. 
 Now calculating the percent yield = (actual x100)/ predicted = 8.7 x100/10.15
 The percent yield = 85.71%.

The correct answer is:

15 bicycles and 6 skateboards.

Explanation:

Let x represent the number of bicycles and y represent the number of skateboards.  The first equation in our system is then

x+y = 21, since there are 21 total items in the shop.

Each bicycle has 2 tires and each skateboard has 4; this gives us the equation

2x+4y=54 (because they are ordering 54 tires).

This makes our system

We will use elimination to solve this; we first need one of the variables to have the same coefficient in both equations.  We will make x the same, and we will do this by multiplying the first equation by 2:

Now we will subtract the second equation from the first one:

Divide both sides by -2:

-2y/-2 = -12/-2

y = 6

There were 6 skateboards.  Substituting this into the first equation,

x+6 = 21

Subtract 6 from each side:

x+6-6 = 21-6

x = 15

There were 15 bicycles.