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Correct Answer: decrease to 1/4th of the original value
the question provided is about the change in pressure when helium gas is transferred from a smaller vessel (250 cm³) to a larger vessel (1 liter, i.e., 1000 cm³) while maintaining a constant temperature (300 k). to solve this, we can apply boyle’s law, which is a fundamental principle in chemistry and physics that describes the inverse relationship between the pressure and volume of a gas at constant temperature.
boyle's law states that the product of the pressure and volume of a fixed amount of an ideal gas, kept at a constant temperature, is constant. mathematically, it is expressed as:
\[ p_1v_1 = p_2v_2 \]
where:
- \(p_1\) and \(v_1\) are the initial pressure and volume of the gas,
- \(p_2\) and \(v_2\) are the final pressure and volume of the gas.
in this scenario:
- the initial volume \(v_1\) is 250 cm³.
- the final volume \(v_2\) is 1000 cm³.
- we need to find the final pressure \(p_2\) given that the initial pressure \(p_1\) is unknown but constant.
substituting the known values into boyle’s law formula, we get:
\[ p_1 \times 250 = p_2 \times 1000 \]
to isolate \(p_2\), we rearrange the equation:
\[ p_2 = \frac{p_1 \times 250}{1000} \]
\[ p_2 = \frac{p_1}{4} \]
this calculation shows that the final pressure \(p_2\) is one fourth of the initial pressure \(p_1\). therefore, when the helium gas is moved from a smaller vessel to a vessel with four times greater capacity, the pressure decreases to one fourth of its original value. this outcome is a direct consequence of boyle’s law, illustrating how pressure decreases as volume increases when temperature is kept constant. this is why the correct answer to the question is that the pressure will "decrease to 1/4th of the original value".
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