Let's solve each problem step by step using the
useful equations provided:
---
Useful Equations:
- 1.00 atm = 101.3 kPa
- 1.00 atm = 760 torr
- 1.00 atm = 14.7 psi
- 1.00 atm = 760 mmHg
Note:
mmHg and torr are equivalent (1 mmHg = 1 torr).
---
Problem 1:
The pressure is recorded as 738 mmHg. Convert this measurement to atmospheres (atm).
We use:
$$
1.00\ \text{atm} = 760\ \text{mmHg}
$$
So:
$$
\text{Pressure in atm} = \frac{738\ \text{mmHg}}{760\ \text{mmHg/atm}} = 0.9709\ \text{atm}
$$
Answer:
$$
\boxed{0.971}\ \text{atm} \quad (\text{rounded to 3 significant figures})
$$
---
Problem 2:
The air pressure in a tire is 2.38 atm. What is this pressure in kilopascals?
We use:
$$
1.00\ \text{atm} = 101.3\ \text{kPa}
$$
So:
$$
\text{Pressure in kPa} = 2.38\ \text{atm} \times 101.3\ \text{kPa/atm} = 241.194\ \text{kPa}
$$
Answer:
$$
\boxed{241}\ \text{kPa} \quad (\text{rounded to 3 significant figures})
$$
---
Problem 3:
The safety disk in a scuba tank will blow at a pressure of approximately 25000 kPa. Convert this pressure to mmHg.
First, convert kPa to atm:
$$
1.00\ \text{atm} = 101.3\ \text{kPa}
\Rightarrow \text{Pressure in atm} = \frac{25000\ \text{kPa}}{101.3\ \text{kPa/atm}} = 246.7\ \text{atm}
$$
Now convert atm to mmHg:
$$
1.00\ \text{atm} = 760\ \text{mmHg}
\Rightarrow 246.7\ \text{atm} \times 760\ \text{mmHg/atm} = 187,592\ \text{mmHg}
$$
Answer:
$$
\boxed{1.88 \times 10^5}\ \text{mmHg} \quad (\text{rounded to 3 significant figures})
$$
---
Problem 4:
The atmosphere supports a column of mercury that is 748 mm in height. What is atmospheric pressure in torr? Convert this pressure to atmospheres (atm).
- Since
1 mmHg = 1 torr, then:
$$
748\ \text{mmHg} = 748\ \text{torr}
$$
Now convert to atm:
$$
\text{Pressure in atm} = \frac{748\ \text{mmHg}}{760\ \text{mmHg/atm}} = 0.9842\ \text{atm}
$$
Answer:
- Pressure in torr: $\boxed{748}\ \text{torr}$
- Pressure in atm: $\boxed{0.984}\ \text{atm}$ (rounded to 3 significant figures)
---
✔ Final Answers:
1. $ \boxed{0.971} $ atm
2. $ \boxed{241} $ kPa
3. $ \boxed{1.88 \times 10^5} $ mmHg
4. $ \boxed{748} $ torr; $ \boxed{0.984} $ atm
Let me know if you'd like these formatted for printing or need explanations in simpler terms!
Parent Tip: Review the logic above to help your child master the concept of pressure conversion worksheet.
