how to convert 5.0 x 10^24 molecules to liters.
The correct answer and explanation is:
To convert 5.0 x 10²⁴ molecules to liters, it is important to understand the relationship between molecules, moles, and volume of a gas.
Step 1: Convert molecules to moles
The number of molecules is converted to moles using Avogadro’s number, which is approximately 6.022 x 10²³ molecules per mole. This constant tells how many molecules are present in one mole of a substance. moles=number of moleculesAvogadro’s number=5.0×10246.022×1023≈8.31 moles\text{moles} = \frac{\text{number of molecules}}{\text{Avogadro’s number}} = \frac{5.0 \times 10^{24}}{6.022 \times 10^{23}} \approx 8.31 \text{ moles}
Step 2: Convert moles to liters
The volume of one mole of an ideal gas at standard temperature and pressure (STP: 0°C and 1 atm) is 22.4 liters. This value is used to convert moles to liters for gases under STP conditions. volume (liters)=moles×22.4 L/mol=8.31×22.4=186.14 liters\text{volume (liters)} = \text{moles} \times 22.4 \, \text{L/mol} = 8.31 \times 22.4 = 186.14 \, \text{liters}
Final answer:
5.0 x 10²⁴ molecules correspond to approximately 186.14 liters of gas at STP.
Explanation:
Molecules are very small particles that make up substances. Counting individual molecules directly is impractical due to their enormous quantity. Therefore, moles are used as a bridge to relate the microscopic world to a measurable scale. Avogadro’s number defines the number of particles in a mole, allowing conversion from molecules to moles.
Once the number of moles is known, it is possible to determine the volume that gas occupies under certain conditions. At STP, one mole of an ideal gas occupies 22.4 liters. This volume is a standard reference and makes it straightforward to convert moles of gas to liters.
This conversion is common in chemistry when dealing with gases, such as in reactions or measurements. Remember, the 22.4 liters per mole applies only at STP. At different temperatures or pressures, the volume would change, and other gas laws like the ideal gas law would be used.
In summary, the conversion from molecules to liters requires two steps: converting molecules to moles using Avogadro’s number, then converting moles to volume using the molar volume of gas at STP.