Question

b. the mass of aluminum used was 108 grams and the mass of aluminum oxide
is more than the mass of aluminum plus the mass of oxygen.
c. the mass of aluminum used was 108 grams and the mass of aluminum oxide
is equal to the mass of the reactants.
d. the mass of aluminum used was 204 grams.

1. when phosphorus reacts with oxygen, diphosphorus pentoxide is formed. a stu

142 grams of diphosphorus pentoxide.
4\text{p} + 5\text{o}_2
ightarrow 2\text{p}_2\text{o}_5
if the mass of phosphorus used was 124 grams, which of the following statemen
correct?
a. the mass of oxygen used was 18 grams.
b. the mass of oxygen used was 32 grams.
c. the mass of oxygen used was 36 grams and the total mass of the reactants
mass of the product.
d. the mass of oxygen used was 18 grams and the total mass of the reactants
mass of the product.

Explanation:

Step1: Recall the law of conservation of mass

The law of conservation of mass states that in a chemical reaction, the total mass of reactants is equal to the total mass of products. The reaction is \(4P + 5O_2 ightarrow2P_2O_5\).

Step2: Calculate the mass of oxygen used

First, we know the mass of phosphorus (\(P\)) used is 124 grams. Let's find the molar mass of \(P\) (atomic mass of \(P\) is approximately 31 g/mol), so 4 moles of \(P\) have a mass of \(4\times31 = 124\) g (which matches the given mass of \(P\) used). Now, for the oxygen: 5 moles of \(O_2\), molar mass of \(O_2\) is \(32\) g/mol, so mass of \(O_2\) is \(5\times32=160\)? Wait, no, wait the product mass: Wait, maybe I made a mistake. Wait the product is \(2P_2O_5\). Wait, let's use the law of conservation of mass directly. Wait, maybe the product mass is given? Wait no, the problem says "a student..." (maybe a typo, but from the reaction, and the mass of \(P\) is 124 g. Wait, let's re - evaluate. Wait, the molar ratio of \(P\) to \(O_2\) in the reaction \(4P+5O_2 ightarrow2P_2O_5\) is 4:5. Molar mass of \(P = 31\) g/mol, so moles of \(P=\frac{124\ g}{31\ g/mol}=4\) moles. Then moles of \(O_2\) needed is 5 moles (from the ratio 4:5). Molar mass of \(O_2 = 32\) g/mol, so mass of \(O_2=5\times32 = 160\)? No, that can't be. Wait, maybe the product mass is 142 g? Wait the text says "142 grams of diphosphorus pentoxide". Oh! So product mass (\(m_{P_2O_5}\)) is 142 g. Then by law of conservation of mass, \(m_P + m_{O_2}=m_{P_2O_5}\). So \(m_{O_2}=m_{P_2O_5}-m_P=142 - 124 = 18\) g? Wait no, 142 - 124 is 18? Wait 124+18 = 142. But wait, the molar ratio: 4 moles of \(P\) (124 g) react with 5 moles of \(O_2\) (160 g) to form 2 moles of \(P_2O_5\) (molar mass of \(P_2O_5=(2\times31)+(5\times16)=62 + 80 = 142\) g/mol, so 2 moles is \(2\times142 = 284\) g). Wait, there is a contradiction here. Wait, maybe the product mass is 142 g (1 mole of \(P_2O_5\))? Then moles of \(P_2O_5=\frac{142\ g}{142\ g/mol}=1\) mole. Then from the reaction, 2 moles of \(P_2O_5\) come from 4 moles of \(P\) and 5 moles of \(O_2\), so 1 mole of \(P_2O_5\) comes from 2 moles of \(P\) and 2.5 moles of \(O_2\). Mass of \(P\) for 2 moles: \(2\times31 = 62\) g, but the problem says mass of \(P\) is 124 g. Wait, maybe the problem has a typo, but let's go with the law of conservation of mass. The law of conservation of mass states that \(m_{reactants}=m_{products}\). So \(m_P + m_{O_2}=m_{P_2O_5}\). Given \(m_P = 124\) g, and if we assume the product mass is 142 g (as per the text "142 grams of diphosphorus pentoxide"), then \(m_{O_2}=142 - 124=18\) g? No, 142 - 124 is 18? Wait 124+18 = 142. But according to the molar masses, 4 moles of \(P\) (124 g) should react with 5 moles of \(O_2\) (160 g) to form 2 moles of \(P_2O_5\) (284 g). So there is a mistake in the problem's product mass? But assuming the product mass is 142 g (maybe it's 1 mole), then \(m_{O_2}=142 - 124 = 18\) g, and total mass of reactants (\(124 + 18=142\)) equals mass of product. So option D says "The mass of oxygen used was 18 grams and the total mass of the reactants equals mass of the product." Wait, but let's check again. Wait, maybe the product mass is 284 g, but the problem says 142 g. Maybe it's a half - reaction. Anyway, using the law of conservation of mass: \(m_{P}+m_{O_2}=m_{P_2O_5}\). So if \(m_P = 124\) g and \(m_{P_2O_5}=142\) g, then \(m_{O_2}=142 - 124 = 18\) g, and \(m_{reactants}=m_{products}\). So option D. Wait, but let's check the options again. Option D: "The mass of oxygen used was 18 grams and the total mass of the reactants equals mass of the product." Option A: 18 g but no mention of reactant - product mass. Option C: 36 g, which is wrong. Option B: 32 g, wrong. So the correct option is D? Wait no, wait 124+18 = 142, which is the product mass. So the law of conservation of mass holds. So the correct statement is D? Wait, but according to the molar ratio, 4 moles of \(P\) (124 g) react with 5 moles of \(O_2\) (160 g) to form 2 moles of \(P_2O_5\) (284 g). So if the product is 142 g (1 mole), then \(P\) used is 2 moles (62 g), but the problem says \(P\) is 124 g (4 moles). So there is an inconsistency. But based on the given numbers in the problem (mass of \(P = 124\) g, mass of \(P_2O_5=142\) g), then \(m_{O_2}=142 - 124 = 18\) g, and total mass of reactants (\(124 + 18\)) equals mass of product (142 g). So option D.

Answer:

D. The mass of oxygen used was 18 grams and the total mass of the reactants equals mass of the product.