WEBVTT
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A vanadium compound has the molecular formula V π₯ O 3, where π₯ is a whole number.
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If the percentage by mass of V in V π₯ O 3 is 68 percent, what is the value of π₯?
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The molar mass of oxygen is 16 grams per mole and vanadium, 51 grams per mole.
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To calculate the percentage by mass, if we assume that weβre calculating the percentage by mass of element A present in substance B, then we need to divide the mass of element A by the mass of substance B and multiply it by 100 percent.
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More specifically for this example, element A will be V, vanadium, and substance B will be V π₯ O 3, vanadium oxide.
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So to find the percent by mass of vanadium in vanadium oxide, we need to divide the mass of vanadium, making sure to include the subscript value, which in this case is π₯, by the mass of vanadium oxide and multiply by 100 percent.
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We have been given the percentage by mass of vanadium in vanadium oxide in the question.
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It is 68 percent.
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To find the mass of vanadium, we can use the molar mass.
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The molar mass of vanadium is 51 grams per mole, so one mole of vanadium is 51 grams.
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Therefore, π₯ moles of vanadium will be π₯ times 51 grams.
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To find the mass of vanadium oxide, we need to use the molar masses of oxygen and vanadium.
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We have already established that π₯ moles of vanadium is π₯ times 51 grams.
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The molar mass of oxygen is 16 grams per mole, so one mole of oxygen is 16 grams.
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We have three equivalents in the molecular formula of vanadium oxide, so we need to multiply three by 16 grams.
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Adding π₯ times 51 grams and three times 16 grams will give us the mass of one mole of vanadium oxide.
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We then need to multiply this by 100 percent.
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Since weβre trying to find the value of π₯, we need to make π₯ the subject.
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But first, letβs simplify this a bit.
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We can divide both sides of the equation by 100 percent to give us 0.68 equals π₯ times 51 grams divided by π₯ times 51 grams plus 48 grams.
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If we multiply both sides of the equation by π₯ times 51 grams plus 48 grams and then multiply the contents of the parentheses by 0.68, then we get 34.68π₯ grams plus 32.64 grams equals 51π₯ grams.
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We need to make π₯ the subject.
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So we need to subtract 34.68π₯ grams from both sides of the equation.
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So 32.64 grams equals 16.32π₯ grams.
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If we divide both sides of the equation by 16.32 grams, we find that π₯ equals two.
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So the answer to the question βIf the percentage by mass of vanadium in vanadium oxide is 68 percent, what is the value of π₯?β is two.