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Sagot :
This is a combined gas law problem, according to which
[tex]\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}[/tex]
where P is the pressure of the gas, V is the volume of the gas, and T is the temperature of the gas, and the subscripts 1 and 2 correspond to the initial and final conditions of the gas. In this problem, we are given the initial pressure, volume, and temperature of the gas in the balloon:
P₁ = 1.0 atm
V₁ = 1.8 L
T₁ = 295.15 K (K = °C + 273.15).
Moreover, we are given the final pressure and temperature of the gas in the balloon.
P₂ = 0.86 atm
T₂ = 281.15 K.
What we want to find is the final volume, V₂, which we can obtain by rearranging the combined gas equation to solve for V₂:
[tex]V_2=\frac{P_1V_1T_2}{T_1P_2} = \frac{(1.0 \text{ atm})(1.8 \text{ L})(281.15 \text{ K})}{(295.15 \text{ K})(0.86 \text{ atm})} \\ V_2 = 1.99 \text{ L}[/tex]
This answer has three significant figures. However, the question as written would warrant an answer that comprises one significant figure (as 8 °C has only one sig fig). In that case, the answer would be 2 L. If the answer is to be given to two significant figures, the volume would then be 2.0 L.
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