help with chemistry

Question

Phosphorus pentoxide (P₄O₁₀; molar mass = 283.89 g/mol; the common name is derived from the empirical formula) is used to produce phosphoric acid for cola soft drinks. It is prepared by burning phosphorus in oxygen. The chemical reaction is given below:

P₄ + 5 O₂  ➜  P₄O₁₀

If 150.0 g of P₄ (molar mass: 123.9 g/mol) and 60.00 g O₂ (molar mass: 31.998 g/mol) are used for the reaction, which of the following statements is TRUE?

Select one:

a.

All reactants are completely used up in the reaction.

b.

13.53 g of O₂ remains.

c.

343.7 g of P₄O₁₀ is formed.

d.

103.5 g of P₄ remains.

Answer 1

To solve this problem we will take the following steps:

step 1: convert grams P4 to moles of P4 and convert grams O2 to moles O2 using molar mass

step 2: convert moles P4 to moles P4O10 and moles O2 to moles P4O10 using the mole ratio

step 3: compare the two values -> if they are the same then the answer is A, and if they are not we will choose the SMALLEST number

step 4: if the answer was not A, we will follow the steps to convert back to grams and choose between either B and C or C and D

STEP 1: grams to moles = divide by molar mass

150.0 g P4 / 123.9 = 1.210654…moles P4 (don’t round, keep many/all decimal places if you can)

60.00 g O2 / 31.998 = 1.875117… moles O2

STEP 2: mol to mol =ratio (what you want /what you have)

1.210654 mol P4 x 1P4O10 / 1P4 = 1.210654 mol P4O10

1.875117 mol O2 x 1P4O10 / 5O2 = 0.375023 mol P4O10

STEP 3: they are not the same, so the answer is not A.

O2 made fewer moles of P4O10, so O2 is the limiting reactant. This means it is also not B because we will completely run out of O2. We are stuck between C and D.

STEP 4:We are only going to make 0.375023 moles P4O10. Let’s use our mole ratio to work backwards to see how much P4 we will use up.

0.375023 moles P4O10 x 1P4 / 1 P4O10 = 0.375023 mol P4 used up. We can convert both of these moles back into grams to figure out how much P4O10 we made and how much P4 we used up.

Convert moles to grams = multiply by molar mass

0.375023 mol P4O10 x 283.89 = 106.465 g P4O10 round to 4 sig figs = 106.5 g P4O10 made

0.374023 mol P4 x 123.9 = 46.465g P4 round to 4 sig figs = 46.47g P4 used up

We made 106.5g P4O10 so the answer is not C

We used 46.47g P4, so let’s subtract that from the original amount to see how much is left:

150.0g P4 - 46.47g P4 = 103.5g P4 leftover

This matches with answer D