The mass of an average blueberry is 0.75 g and the mass of an automobile is 2.0×10 3 kg. Find the number of automobiles whose total mass is the same as 1.0 mol of blueberries.

Hey everyone, we're asked how many light duty trucks have the same way as one mole of apples, assuming that a light duty truck weighs 2.7 times 10 to the third kilogram and one apple weighs 144 g, Essentially we're going to have to find the relationship between the two. So let's go ahead and start off with our one mole of Apple. We've learned that we can use avocados number for instances like this, So per one mole of apple, we have 6.22 times 10 to the 23rd apples. Again, this is avocados number. And in our questions then we were also told that for one apple, We have 144 g. Now relating this to our light duty truck, we can see that it weighs in kilograms. So let's go ahead and convert this into kilograms. So we know 10 to the third grams is equivalent to one kg and now we can input our 2.7 times 10 to the third kilograms, which we know Is equivalent to one light duty truck. So when we calculate this out and cancel out our units, We're going to end up with a value of 3.2 Times 10 to the 19 light duty trucks and this is going to be our final answer. So I hope this made sense. And let us know if you have any questions

Ch.2 - Atoms & Elements

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Tro 5th Edition

Ch.2 - Atoms & Elements

Problem 110

Chapter 2, Problem 110

The mass of an average blueberry is 0.75 g and the mass of an automobile is 2.0×10³ kg. Find the number of automobiles whose total mass is the same as 1.0 mol of blueberries.

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Determine the mass of 1.0 mol of blueberries. Since the molar mass of a substance is the mass of 6.022 x 10^23 particles (Avogadro's number), multiply the mass of one blueberry by Avogadro's number to find the mass of 1.0 mol of blueberries.

Convert the mass of the automobile from kilograms to grams for consistency in units, as the mass of the blueberry is given in grams. Recall that 1 kg equals 1000 grams.

Calculate the total mass of 1.0 mol of blueberries in grams using the conversion from step 1.

Divide the total mass of 1.0 mol of blueberries by the mass of one automobile (converted to grams in step 2) to find the number of automobiles needed to equal this mass.

Ensure all units are consistent and check calculations for accuracy to ensure the correct number of automobiles is determined.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). For blueberries, the average mass is 0.75 g, which means that one mole of blueberries would weigh 0.75 g multiplied by Avogadro's number (approximately 6.022 x 10^23), allowing us to calculate the total mass of 1.0 mol of blueberries.

Unit Conversion

Unit conversion is the process of converting a quantity expressed in one set of units to another. In this problem, we need to convert the mass of the automobile from kilograms to grams (1 kg = 1000 g) to facilitate a direct comparison with the mass of blueberries, ensuring that both quantities are expressed in the same unit.

Ratio and Proportion

Ratio and proportion involve comparing two quantities to determine how many times one quantity contains another. In this context, once we have the total mass of 1.0 mol of blueberries and the mass of a single automobile, we can set up a ratio to find out how many automobiles would equal the total mass of the blueberries, allowing us to solve the problem effectively.

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Carbon-12 contains six protons and six neutrons. The radius of the nucleus is approximately 2.7 fm (femtometers) and the radius of the atom is approximately 70 pm (picometers). What percentage of the carbon atom's volume is occupied by the nucleus? (Assume two significant figures.)

Textbook Question

A penny has a thickness of approximately 1.0 mm. If you stacked Avogadro's number of pennies one on top of the other on Earth's surface, how far would the stack extend (in km)? [For comparison, the sun is about 150 million km from Earth and the nearest star (Proxima Centauri) is about 40 trillion km from Earth.]

Textbook Question

Consider the stack of pennies in the previous problem. How much money (in dollars) would this represent? If this money were equally distributed among the world's population of 7.0 billion people, how much would each person receive? Would each person be a millionaire? A billionaire? A trillionaire?

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A pure titanium cube has an edge length of 2.78 in. How many titanium atoms does it contain? Titanium has a density of 4.50 g/cm³.

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A pure copper sphere has a radius of 0.935 in. How many copper atoms does it contain? [The volume of a sphere is (4/3)πr³ and the density of copper is 8.96 g/cm³.]

The mass of an average blueberry is 0.75 g and the mass of an automobile is 2.0×103 kg. Find the number of automobiles whose total mass is the same as 1.0 mol of blueberries.

Verified video answer for a similar problem:

Key Concepts

Molar Mass

Unit Conversion

Ratio and Proportion

The mass of an average blueberry is 0.75 g and the mass of an automobile is 2.0×10³ kg. Find the number of automobiles whose total mass is the same as 1.0 mol of blueberries.