One M&M candy has a volume of 1.0mL. What volume, in cubic meters, would one mole of M&M candies occupy?
2) For this next calculation, you’re going to compare the volume of a mole of M&Ms to Lake Erie, which has a volume of 116mi^3. How many lakes the size of Lake Erie would a mole of M&M candies fill?
3) A package of 50 M&M candies costs 50 cents. How much would a mole of M&Ms cost, in dollars? Given that the annual budget of the United States is approximately two trillion dollars ($2 X 10^12), how many years would it take for the US to pay for a mole of M&Ms?
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I will do the first one for you to get you started.
1 M&M = 1.0 mL; therefore, 1 mole of M^Ms will be 6.022 x 10^23 mL = 6.022 x 10^23 cc. Tjere are 1 x 10^6 cc in 1 m^3.
6.022 x 10^23 cc x (1 m^3/1 x 10^6 cc) = ?? m^3.
1. To calculate the volume of one mole of M&M candies in cubic meters, we first need to determine the number of M&M candies in one mole.
According to Avogadro's constant, one mole of any substance contains 6.022 x 10^23 particles. Therefore, one mole of M&M candies would also contain 6.022 x 10^23 candies.
Given that each M&M candy has a volume of 1.0 mL, we can convert this to cubic meters by multiplying by the appropriate conversion factors.
1 mL = 1 x 10^-6 m^3 (since there are 1,000,000 mL in a cubic meter)
1 mole of M&M candies = 6.022 x 10^23 candies
Thus, the volume of one mole of M&M candies in cubic meters is:
Volume = (1.0 mL/candy) x (6.022 x 10^23 candies) x (1 x 10^-6 m^3/mL)
Volume ≈ 6.022 x 10^17 m^3
2. To calculate how many lakes the size of Lake Erie a mole of M&M candies would fill, we need to determine the volume of a mole of M&M candies in cubic miles and then compare it to the volume of Lake Erie.
Given that 1 mile (mi) is approximately equal to 1.609344 kilometers (km), we can calculate the volume of a mole of M&M candies in cubic kilometers:
Volume = (1.0 mL/candy) x (6.022 x 10^23 candies) x (1 x 10^-6 km^3/mL)
Volume ≈ 6.022 x 10^17 km^3
Then, we convert this volume to cubic miles:
1 km^3 ≈ 0.386102 cubic miles (since 1 km^3 is approximately equal to 0.386102 mi^3)
Volume ≈ (6.022 x 10^17 km^3) x (0.386102 mi^3/km^3)
Volume ≈ 2.32 x 10^17 mi^3
Now, we can determine how many lakes the size of Lake Erie this volume would fill:
Number of lakes ≈ (Volume of M&Ms) / (Volume of Lake Erie)
Number of lakes ≈ (2.32 x 10^17 mi^3) / (116 mi^3)
Number of lakes ≈ 2 x 10^15
Therefore, a mole of M&M candies would fill approximately 2 x 10^15 lakes the size of Lake Erie.
3. To calculate the cost of a mole of M&M candies in dollars, we first need to determine the cost of 50 candies (as given in the question). Since a package of 50 M&M candies costs 50 cents, the cost per candy would be:
Cost per candy = 50 cents / 50 candies
Cost per candy = 1 cent (since 1 cent = $0.01)
Now, we can calculate the cost of a mole of M&M candies:
Cost = (1 cent/candy) x (6.022 x 10^23 candies)
Cost ≈ 6.022 x 10^21 cents
To convert this to dollars, we divide by 100 since there are 100 cents in a dollar:
Cost ≈ (6.022 x 10^21 cents) / 100
Cost ≈ 6.022 x 10^19 dollars
Given that the annual budget of the United States is approximately two trillion dollars ($2 x 10^12), we can calculate how many years it would take for the US to pay for a mole of M&Ms:
Years ≈ (Cost of a mole of M&Ms) / (Annual budget of the US)
Years ≈ (6.022 x 10^19 dollars) / ($2 x 10^12)
Years ≈ 3.011 x 10^7 years
Therefore, it would take approximately 30,110,000 years for the US to pay for a mole of M&M candies.
To answer these questions, we need to use some conversion factors and calculations. Let's break it down step by step:
1) Volume of one M&M candy: 1.0 mL
To find the volume of one mole of M&M candies in cubic meters, we need the molar volume of a substance. The molar volume is the volume occupied by one mole of a substance.
The molar volume of any gas at standard temperature and pressure (STP) is 22.4 liters or 0.0224 cubic meters. However, M&M candies are solid, so we need to use a different approach.
Since we know the volume of one M&M candy (1.0 mL), we can convert it to cubic meters by dividing by 1,000,000 (since there are 1,000,000 cubic meters in a liter).
1.0 mL = 1.0 × 10^(-6) cubic meters
Therefore, one mole of M&M candies would occupy a volume of 1.0 × 10^(-6) cubic meters.
2) Volume of Lake Erie: 116 mi^3
To determine how many lakes the size of Lake Erie would be filled by one mole of M&M candies, we need to calculate the ratio of their volumes.
First, we have to convert the volume of Lake Erie from cubic miles to cubic meters. Since 1 mile is approximately 1,609.34 meters, we can use this conversion factor.
1 mi^3 = (1.60934 km)^3 = 4.168181 × 10^9 m^3
Now that we know the volume of Lake Erie in cubic meters, we can calculate the number of lakes:
Number of lakes = (Volume of Lake Erie) / (Volume of one mole of M&M candies)
Number of lakes = 4.168181 × 10^9 m^3 / (1.0 × 10^(-6) m^3)
Calculating this will give us the number of lakes that one mole of M&M candies would fill.
3) Cost of one package of 50 M&M candies: $0.50
To determine the cost of a mole of M&M candies, we need to calculate the number of packages required, considering there are 50 candies in each package.
Number of packages = (Total number of M&M candies in one mole) / (Number of M&M candies in one package)
Number of packages = (6.02214 × 10^23) / 50
Next, multiply the cost of one package by the number of packages:
Cost of a mole of M&M candies = (Number of packages) × (Cost of one package)
Finally, to determine how many years it would take for the US to pay for a mole of M&M candies, we need to calculate the number of moles of M&Ms that can be bought with the US annual budget.
Number of moles of M&M candies = (US annual budget) / (Cost of a mole of M&M candies)
Number of years = (Number of moles of M&M candies) / (moles consumed per year)
Please note that to calculate the exact answers, you'll need to input the given values (such as the volume of Lake Erie and the cost of one package of M&Ms) into the calculations.