Answer: It will occupy [tex]4.45\times 10^3ml[/tex] at the same temperature and 475 mm Hg.
Explanation:
Boyle's Law: This law states that pressure is inversely proportional to the volume of the gas at constant temperature and number of moles.
[tex]P\propto \frac{1}{V}[/tex] (At constant temperature and number of moles)
[tex]P_1V_1=P_2V_2[/tex] (At constant temperature and number of moles)
where,
[tex]P_1[/tex] = initial pressure of gas = 760 mm Hg
[tex]P_2[/tex] = final pressure of gas = 475 mm Hg
[tex]V_1[/tex] = initial volume of gas = [tex]2.78\times 10^3ml[/tex]
[tex]V_2[/tex] = final volume of gas = ?
Putting in the values:
[tex]760mm Hg\times 2.78\times 10^3ml=475 mm Hg\times V_2[/tex]
[tex]V_2=4.45\times 10^3ml[/tex]
Thus it will occupy [tex]4.45\times 10^3ml[/tex] at the same temperature and 475 mm Hg
The volume that it will occupy at the same temperature is 4448mL
According to Boyle's law, the pressure of a given mass of gas is inversely proportional to the volume. It is expressed mathematically as:
[tex]P\alpha\frac{1}{V}\\P=\frac{k}{V}\\PV=k[/tex]
This can be expressed as [tex]P_1V_1=P_2V_2[/tex]
Given the following parameters
P₁ = 760mmHg
V₁ = 2.78 x 10³ mL
P₂ = 475mmHg
V₂ = ?
Substitute the given parameters into the formula
[tex]V_2=\frac{P_1V_1}{P_2}\\V_2=\frac{760\times 2780}{475}\\V_2= 4448mL[/tex]
Hence the volume that it will occupy at the same temperature is 4448mL
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