dimensional analysis (unit factor method)\nusing this method, it is possible to solve many problems by using…

dimensional analysis (unit factor method)\nusing this method, it is possible to solve many problems by using the relationship of one unit to another. for example, 12 inches = one foot. since these two numbers represent the same value, the fractions 12 in./1 ft. and 1 ft./12 in. are both equal to one. when you multiply another number by the number one, you do not change its value. however, you may change its unit.\nexample 1: convert 2 miles to inches.\n2 miles×5280 ft./1 mile×12 inches/1 ft.=126720 in.\nexample 2: how many seconds are in 4 days?\n4 days×24 hr./1 day×60 min./1 hr.×60 sec./1 min.=345600 sec.\nsolve each problem. round irrational numbers to the thousandths place.\n1. 3 hr. = ______________ sec.\n2. 0.035 mg = ______________ cg\n3. 5.5 kg = ______________ lb.\n4. 2.5 yd. = ______________ in.\n5. 1.3 yr. = ______________ hr.\n6. 3 moles = ______________ molecules (1 mole = 6.02×10²³ molecules)\n7. 2.5×10²⁴ molecules = ______________ moles\n8. 5 moles = ______________ liters (1 mole = 22.4 liters)\n9. 100. liters = ______________ moles\n10. 50. liters = ______________ molecules\n11. 5.0×10²⁴ molecules = ______________ liters\n12. 7.5×10³ ml = ______________ liters

dimensional analysis (unit factor method)\nusing this method, it is possible to solve many problems by using the relationship of one unit to another. for example, 12 inches = one foot. since these two numbers represent the same value, the fractions 12 in./1 ft. and 1 ft./12 in. are both equal to one. when you multiply another number by the number one, you do not change its value. however, you may change its unit.\nexample 1: convert 2 miles to inches.\n2 miles×5280 ft./1 mile×12 inches/1 ft.=126720 in.\nexample 2: how many seconds are in 4 days?\n4 days×24 hr./1 day×60 min./1 hr.×60 sec./1 min.=345600 sec.\nsolve each problem. round irrational numbers to the thousandths place.\n1. 3 hr. = ______________ sec.\n2. 0.035 mg = ______________ cg\n3. 5.5 kg = ______________ lb.\n4. 2.5 yd. = ______________ in.\n5. 1.3 yr. = ______________ hr.\n6. 3 moles = ______________ molecules (1 mole = 6.02×10²³ molecules)\n7. 2.5×10²⁴ molecules = ______________ moles\n8. 5 moles = ______________ liters (1 mole = 22.4 liters)\n9. 100. liters = ______________ moles\n10. 50. liters = ______________ molecules\n11. 5.0×10²⁴ molecules = ______________ liters\n12. 7.5×10³ ml = ______________ liters

Answer

Explanation:

Step1: Convert hours to seconds

We know that 1 hour = 3600 seconds. So for 3 hours, we multiply 3 by 3600. $3\times3600 = 10800$

Step2: Convert milligrams to centigrams

Since 1 centigram = 10 milligrams, to convert 0.035 mg to cg, we divide 0.035 by 10. $0.035\div10=0.0035$

Step3: Convert kilograms to pounds

1 kg is approximately 2.205 lb. For 5.5 kg, we multiply 5.5 by 2.205. $5.5\times2.205 = 12.1275\approx12.128$

Step4: Convert yards to inches

1 yard = 36 inches. For 2.5 yards, we multiply 2.5 by 36. $2.5\times36=90$

Step5: Convert years to hours

1 year has 365 days (ignoring leap - years for simplicity), 1 day has 24 hours. For 1.3 years, we calculate $1.3\times365\times24$. $1.3\times365\times24=11388$

Step6: Convert moles to molecules

1 mole = $6.02\times10^{23}$ molecules. For 3 moles, we multiply 3 by $6.02\times10^{23}$. $3\times6.02\times10^{23}=1.806\times 10^{24}$

Step7: Convert molecules to moles

If 1 mole = $6.02\times10^{23}$ molecules, then for $2.5\times10^{24}$ molecules, we divide by $6.02\times10^{23}$. $\frac{2.5\times10^{24}}{6.02\times10^{23}}\approx4.153$

Step8: Convert moles to liters

1 mole = 22.4 liters. For 5 moles, we multiply 5 by 22.4. $5\times22.4 = 112$

Step9: Convert liters to moles

If 1 mole = 22.4 liters, then for 100 liters, we divide 100 by 22.4. $\frac{100}{22.4}\approx4.464$

Step10: Convert liters to molecules

First, find moles from liters. If 1 mole = 22.4 liters, for 50 liters, the number of moles is $\frac{50}{22.4}$. Then convert moles to molecules. Number of moles $n=\frac{50}{22.4}\approx2.232$ Number of molecules $=2.232\times6.02\times10^{23}\approx1.344\times10^{24}$

Step11: Convert molecules to liters

First, find moles from molecules. If 1 mole = $6.02\times10^{23}$ molecules, for $5.0\times10^{24}$ molecules, the number of moles is $\frac{5.0\times10^{24}}{6.02\times10^{23}}\approx8.306$. Then convert moles to liters. Number of liters $=8.306\times22.4\approx186.054$

Step12: Convert milliliters to liters

Since 1 liter = 1000 mL, for $7.5\times10^{3}$ mL, we divide by 1000. $\frac{7.5\times10^{3}}{1000}=7.5$

Answer:

  1. 10800
  2. 0.0035
  3. 12.128
  4. 90
  5. 11388
  6. $1.806\times 10^{24}$
  7. 4.153
  8. 112
  9. 4.464
  10. $1.344\times10^{24}$
  11. 186.054
  12. 7.5