QuestionJune 7, 2025

Part I: Unit Conversions.Show all work (known and unknown, and dimensional analysis - including units! Write your answers in the boxes provided. Unit Test: Dimensional Analysis and Mole Convers 1. Find the number of minutes in 25 years, assuming that 1year=365days K:25 years 2. The driving distance from Spokane to Seattle is 479,000 meters. Convert this distance to miles given 1m=100cm,1in=2.54cm,12in=1ft, and 1mi=5280ft square Part II: Mole Conversions . Show all work (known and unknown, and dimensional analysis - including units! Write your answers in the boxes provided. 3. A sample contains 9.2times 10^22 atoms of beryllium (Be)How many moles is this? square 4. The formula for Aluminum Carbonate is Al_(2)(CO_(3))_(3) What is the molar mass of aluminum carbonate? square

Part I: Unit Conversions.Show all work (known and unknown, and dimensional analysis - including units! Write your answers in the boxes provided. Unit Test: Dimensional Analysis and Mole Convers 1. Find the number of minutes in 25 years, assuming that 1year=365days K:25 years 2. The driving distance from Spokane to Seattle is 479,000 meters. Convert this distance to miles given 1m=100cm,1in=2.54cm,12in=1ft, and 1mi=5280ft square Part II: Mole Conversions . Show all work (known and unknown, and dimensional analysis - including units! Write your answers in the boxes provided. 3. A sample contains 9.2times 10^22 atoms of beryllium (Be)How many moles is this? square 4. The formula for Aluminum Carbonate is Al_(2)(CO_(3))_(3) What is the molar mass of aluminum carbonate? square
Part I: Unit Conversions.Show all work (known and unknown, and dimensional analysis - including units! Write your answers in the boxes provided. Unit Test: Dimensional Analysis and Mole Convers 1. Find the number of minutes in 25 years, assuming that 1year=365days K:25 years 2. The driving distance from Spokane to Seattle is 479,000 meters. Convert this distance to miles given 1m=100cm,1in=2.54cm,12in=1ft, and 1mi=5280ft square Part II: Mole Conversions . Show all work (known and unknown, and dimensional analysis - including units! Write your answers in the boxes provided. 3. A sample contains 9.2times 10^22 atoms of beryllium (Be)How many moles is this? square 4. The formula for Aluminum Carbonate is Al_(2)(CO_(3))_(3) What is the molar mass of aluminum carbonate? square

Solution
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Answer

1. Convert years to days ### 25 \text{ years} \times 365 \text{ days/year} = 9125 \text{ days} ## Step2: Convert days to hours ### 9125 \text{ days} \times 24 \text{ hours/day} = 219,000 \text{ hours} ## Step3: Convert hours to minutes ### 219,000 \text{ hours} \times 60 \text{ minutes/hour} = 13,140,000 \text{ minutes} # Answer: ### 13,140,000 minutes # Explanation: ## Step1: Convert meters to centimeters ### 479,000 \text{ m} \times 100 \text{ cm/m} = 47,900,000 \text{ cm} ## Step2: Convert centimeters to inches ### 47,900,000 \text{ cm} \div 2.54 \text{ cm/in} = 18,858,267.72 \text{ in} ## Step3: Convert inches to feet ### 18,858,267.72 \text{ in} \div 12 \text{ in/ft} = 1,571,522.31 \text{ ft} ## Step4: Convert feet to miles ### 1,571,522.31 \text{ ft} \div 5280 \text{ ft/mi} = 297.67 \text{ mi} # Answer: ### 297.67 miles # Explanation: ## Step1: Use Avogadro's number for mole conversion ### **Number of moles** = \frac{\text{Number of atoms}}{\text{Avogadro's number}} ## Step2: Calculate moles of beryllium ### \frac{9.2 \times 10^{22} \text{ atoms}}{6.022 \times 10^{23} \text{ atoms/mol}} = 0.1527 \text{ moles} # Answer: ### 0.1527 moles # Explanation: ## Step1: Calculate molar mass of Aluminum (Al) ### 2 \times 26.98 \text{ g/mol} = 53.96 \text{ g/mol} ## Step2: Calculate molar mass of Carbonate (CO₃) ### 3 \times (12.01 + 3 \times 16.00) \text{ g/mol} = 3 \times 60.01 \text{ g/mol} = 180.03 \text{ g/mol} ## Step3: Sum the molar masses ### 53.96 \text{ g/mol} + 180.03 \text{ g/mol} = 233.99 \text{ g/mol} # Answer: ### 233.99 g/mol
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