Question

An oxygen tank contains oxygen \(\left(\mathrm{O}_{2}\right)\) at a pressure of \(2.00 \mathrm{~atm} .\) What is the pressure in the tank in terms of the following units? a. torr b. \(\mathrm{mmHg}\)

Short answer

1520 \mathrm{~torr}; 1520 \mathrm{~mmHg}

Step-by-step solution

- Identify the given pressure

The pressure of oxygen \(\left(\mathrm{O}_{2}\right)\) in the tank is given as \(2.00 \mathrm{~atm}.\)

- Understand the conversions

Remember that \(1 \mathrm{~atm} = 760 \mathrm{~torr}\) and \(1 \mathrm{~torr} = 1 \mathrm{~mmHg}\).

- Convert atm to torr

Multiply the given pressure in \(\mathrm{~atm}\) by the conversion factor to get the pressure in \(\mathrm{~torr}\).\[2.00 ~\mathrm{~atm} \times 760 ~\mathrm{~torr/atm} = 1520 ~\mathrm{~torr} \]

- Convert atm to mmHg

Since \(1~\mathrm{~torr} = 1~\mathrm{~mmHg}\), the pressure in \(\mathrm{~mmHg}\) will be the same as in \(\mathrm{~torr}\). Therefore, the pressure is \1520 \mathrm{~mmHg}.\

Key concepts

atm to torr conversion

Atmosphere (abbreviated as atm) and torr are both units of pressure. In many scientific contexts, converting these units is necessary for precise calculations and comparisons.
One atmosphere is defined as equal to 760 torr.
So, if you need to convert a pressure value from atm to torr, you can do this by multiplying the pressure in atm by 760. This makes sense, because you are scaling up from a larger unit to a smaller unit. For example:
If you have a pressure of 2.00 atm and you want to convert it to torr, the calculation would be:
\[2.00 ~ atm \times 760 ~ \frac{torr}{atm} = 1520 ~ torr\]Now, it's clear: 2.00 atm is equal to 1520 torr.

atm to mmHg conversion

Understanding the relationship between atmospheres (atm) and millimeters of mercury (mmHg) is crucial in many fields, such as chemistry and medicine.
One atmosphere (atm) is defined as 760 mmHg. This unit comes from the historical use of mercury in pressure measurement instruments, like barometers.
Since the relationship between torr and mmHg is direct (1 torr = 1 mmHg), converting from atm to mmHg follows the same process as converting atm to torr.
For a given pressure of 2.00 atm, the conversion to mmHg would be:
\[2.00 ~ atm \times 760 ~ \frac{mmHg}{atm} = 1520 ~ mmHg\]Hence, 2.00 atm is equal to 1520 mmHg.

gas laws

Gas laws are fundamental in understanding the behavior of gases under different conditions of pressure, volume, and temperature.
Here are some key gas laws:

• Boyle's Law: This law describes how the pressure of a gas tends to increase as the volume of the container decreases, provided the temperature and amount of gas remain constant. It can be represented as: \[ P_1V_1 = P_2V_2\]
• Charles's Law: This law states that the volume of a gas is directly proportional to its temperature (in kelvin) when the pressure and amount of gas are constant: \[ \frac{V_1}{T_1} = \frac{V_2}{T_2}\]
• Avogadro's Law: This principle explains that the volume of a gas is directly proportional to the amount of gas (in moles) when the pressure and temperature remain constant: \[ \frac{V_1}{n_1} = \frac{V_2}{n_2}\]

These laws are cornerstones for understanding more complex concepts like the Ideal Gas Law, which combines them into a single equation: \[ PV = nRT\]