A sample of hydrogen gas at a pressure of 903 torr and a temperature of 26.9°C, occupies a volume of 692 mL. If the gas is allowed to expand at constant temperature until its pressure is 633 torr, the volume of the gas sample will be | mL.
Ideal and Real Gases
Ideal gases obey conditions of the general gas laws under all states of pressure and temperature. Ideal gases are also named perfect gases. The attributes of ideal gases are as follows,
Gas Laws
Gas laws describe the ways in which volume, temperature, pressure, and other conditions correlate when matter is in a gaseous state. The very first observations about the physical properties of gases was made by Robert Boyle in 1662. Later discoveries were made by Charles, Gay-Lussac, Avogadro, and others. Eventually, these observations were combined to produce the ideal gas law.
Gaseous State
It is well known that matter exists in different forms in our surroundings. There are five known states of matter, such as solids, gases, liquids, plasma and Bose-Einstein condensate. The last two are known newly in the recent days. Thus, the detailed forms of matter studied are solids, gases and liquids. The best example of a substance that is present in different states is water. It is solid ice, gaseous vapor or steam and liquid water depending on the temperature and pressure conditions. This is due to the difference in the intermolecular forces and distances. The occurrence of three different phases is due to the difference in the two major forces, the force which tends to tightly hold molecules i.e., forces of attraction and the disruptive forces obtained from the thermal energy of molecules.
![**Problem Statement:**
A sample of hydrogen gas at a pressure of 903 torr and a temperature of 26.9°C occupies a volume of 692 mL. If the gas is allowed to expand at constant temperature until its pressure is 633 torr, the volume of the gas sample will be ______ mL.
**Explanation:**
This problem involves the relationship between the pressure and volume of a gas at constant temperature, described by Boyle's Law. Boyle's Law states that the pressure of a given mass of gas is inversely proportional to its volume at a constant temperature:
\[ P_1 V_1 = P_2 V_2 \]
Where:
- \( P_1 \) = initial pressure (903 torr)
- \( V_1 \) = initial volume (692 mL)
- \( P_2 \) = final pressure (633 torr)
- \( V_2 \) = final volume (unknown)
By rearranging the formula to solve for \( V_2 \), we get:
\[ V_2 = \frac{P_1 V_1}{P_2} \]
Substituting the given values:
\[ V_2 = \frac{903 \, \text{torr} \times 692 \, \text{mL}}{633 \, \text{torr}} \]
Calculating the result:
\[ V_2 \approx 987 \, \text{mL} \]
Therefore, the volume of the gas sample when it expands at the constant temperature until its pressure is 633 torr will be approximately 987 mL.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa527ffdc-16df-4a1f-9953-96956a75d05e%2F9b008f8d-18b3-4623-99c8-b310db31f6b1%2Fo364ohg.png&w=3840&q=75)
According to ideal gas law,
PV = nRT
where P = pressure
V = volume
n = moles
R = gas constant
T = temperature in K = T in °C + 273
Since the temperature is given constant. And also no change in moles of gas happening
Hence n and T are constant
Hence PV = nRT = constant
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