In a bank there are as many coins as the number of molecules in 1.6ug of methane. How many coins are there in the 4 bank?
To solve this problem, we need to follow a series of steps. Let's break it down:
Step 1: Determine the number of molecules in 1.6ug of methane
- Methane's molecular formula is CH4, which means it contains 1 carbon (C) atom and 4 hydrogen (H) atoms.
- The molecular mass of carbon is 12 g/mol, and hydrogen is 1 g/mol.
- The molecular mass of methane can be calculated as: (12 g/mol × 1) + (1 g/mol × 4) = 12 + 4 = 16 g/mol.
- Since there are 1.6ug (micrograms) of methane, we need to convert it to grams by dividing it by 1,000,000.
- Therefore, 1.6ug ÷ 1,000,000 = 0.0000016 g.
- We can now calculate how many moles of methane we have by dividing the mass by the molar mass: 0.0000016 g ÷ 16 g/mol = 0.0000001 mol.
- The molar quantity of methane is equal to Avogadro's number (6.022 × 10^23) times the number of moles: 0.0000001 mol × 6.022 × 10^23 = 6.022 × 10^17 molecules.
Step 2: Calculate the number of coins in one bank
- The number of coins in one bank is stated to be equal to the number of methane molecules in 1.6ug.
- So, there are 6.022 × 10^17 coins in one bank.
Step 3: Determine the total number of coins in 4 banks
- To find the total number of coins in 4 banks, we multiply the number of coins in one bank by 4.
- Therefore, 6.022 × 10^17 coins × 4 = 2.4088 × 10^18 coins.
So, there are approximately 2.4088 × 10^18 coins in the 4 banks.