Question

1. convert 3.5 kcal to joules, then to kilojoules.
2. how many milligrams are in 0.025 kilograms?
3. convert 0.5 moles of water to molecules, then to atoms.
4. how many seconds are in 2 days?
5. convert 120 cm to meters, then to millimeters.

answers

1. 1.204 × 10²⁴ molecules, 2) 1.158 atm, 3) 33.01 g, 4) 0.0025 m³, 5) 2.0 moles,
2. 14,644 j → 14.64 kj, 7) 25,000 mg, 8) 9.033 × 10²³ molecules → 2.71 × 10²⁴
3. 172,800 seconds, 10) 1.2 m → 1200 mm

Explanation:

Step1: Convert kcal to joules

We know that \(1\ kcal = 4184\ J\).
So for \(3.5\ kcal\), we have \(3.5\times4184\ J\).

$$3.5\times4184 = 14644\ J$$

Step2: Convert joules to kilojoules

Since \(1\ kJ=1000\ J\), then \(14644\ J=\frac{14644}{1000}\ kJ\).

$$14644\div1000 = 14.644\ kJ$$

Step1: Convert kilograms to grams

We know that \(1\ kg = 1000\ g\).
For \(0.025\ kg\), we have \(0.025\times1000\ g\).

$$0.025\times1000=25\ g$$

Step2: Convert grams to milligrams

Since \(1\ g = 1000\ mg\), then \(25\ g = 25\times1000\ mg\).

$$25\times1000 = 25000\ mg$$

Step1: Convert moles to molecules

We use Avogadro's number \(N_A=6.022\times 10^{23}\ molecules/mol\).
For \(0.5\ mol\) of water, the number of molecules \(n = 0.5\times6.022\times 10^{23}\).

$$n=3.011\times 10^{23}\ molecules$$

Step2: Convert molecules to atoms

Each water molecule (\(H_2O\)) has \(3\) atoms (\(2\) H and \(1\) O).
So the number of atoms \(N = 3\times3.011\times 10^{23}\).

$$N = 9.033\times 10^{23}\ atoms$$

Step1: Convert days to hours

We know that \(1\ day=24\ hours\).
For \(2\) days, we have \(2\times24\ hours\).

$$2\times24 = 48\ hours$$

Step2: Convert hours to minutes

Since \(1\ hour = 60\ minutes\), then \(48\ hours=48\times60\ minutes\).

$$48\times60 = 2880\ minutes$$

Step3: Convert minutes to seconds

Since \(1\ minute = 60\ seconds\), then \(2880\ minutes=2880\times60\ seconds\).

$$2880\times60=172800\ seconds$$

Answer:

\(14644\ J\) and \(14.644\ kJ\)