Question

solve the following problems. write the answers in significant figures.

1. 3 hrs = ______ sec
2. 0.035 mg = ______ cg
3. 5.5 kg = ______ lbs
4. 2.5 yds = ______ in
5. 1.3 yrs = ______ hr (1 yr = 365 days)
6. 3 moles = ______ molecules (1 mole = 6.02 x 10²³ molecules)
7. 2.5 x 10²⁴ molecules = ______ moles
8. 5 moles = ______ liters (1 mole = 22.4 liters)
9. 100. liters = ______ moles
10. 50. liters = ______ molecules
11. 5.0 x 10²⁴ molecules = ______ liters
12. 7.5 x 10³ ml = ______ liters

Explanation:

Step1: Convert hours to seconds

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

Step2: Convert milligrams to centigrams

Since 1 mg = 0.1 cg, for 0.035 mg, we multiply 0.035 by 0.1.
$0.035\times0.1=0.0035$ cg

Step3: Convert kilograms to pounds

1 kg is approximately 2.20462 lbs. For 5.5 kg, we multiply 5.5 by 2.20462.
$5.5\times2.20462 = 12.12541\approx12.1$ lbs

Step4: Convert yards to inches

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

Step5: Convert years to hours

1 year = 365 days and 1 day = 24 hours. So for 1.3 years, we calculate $1.3\times365\times24$.
$1.3\times365\times24=1.3\times8760 = 11388$ hours

Step6: Convert moles to molecules

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

Step7: Convert molecules to moles

If 1 mole = $6.02\times10^{23}$ molecules, then for $2.5\times10^{24}$ molecules, we divide by $6.02\times10^{23}$.
$\frac{2.5\times10^{24}}{6.02\times10^{23}}\approx4.15$ moles

Step8: Convert moles to liters

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

Step9: Convert liters to moles

If 1 mole = 22.4 liters, then for 100 liters, we divide 100 by 22.4.
$\frac{100}{22.4}\approx4.46$ moles

Step10: Convert liters to molecules

First, convert liters to moles ($\frac{50}{22.4}$ moles), then convert moles to molecules by multiplying by $6.02\times10^{23}$.
$\frac{50}{22.4}\times6.02\times10^{23}\approx1.34\times10^{24}$ molecules

Step11: Convert molecules to liters

First, convert molecules to moles ($\frac{5.0\times10^{24}}{6.02\times10^{23}}$ moles), then convert moles to liters by multiplying by 22.4.
$\frac{5.0\times10^{24}}{6.02\times10^{23}}\times22.4\approx186$ liters

Step12: Convert milliliters to liters

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

Answer:

1. 10800
2. 0.0035
3. 12.1
4. 90
5. 11388
6. $1.806\times 10^{24}$
7. 4.15
8. 112
9. 4.46
10. $1.34\times10^{24}$
11. 186
12. 7.5