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At a c onstant t emperature, the volume of a gas is inversely proportional to its pressure. 2.8times 10^6 Pascals and a volume of 1.7times 10^-8m^3 a) What will the volume of the gas be when it s pressure is 6.4times 10^4 Pasc als ? b) Work out the pre ssure of the gas when its volume is 8.7times 10^-9m^3 Give each of your an swers in st andard

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At a c onstant t emperature, the volume of a gas is inversely proportional to its pressure. 2.8times 10^6 Pascals and a volume of 1.7times 10^-8m^3 a) What will the volume of the gas be when it s pressure is 6.4times 10^4 Pasc als ? b) Work out the pre ssure of the gas when its volume is 8.7times 10^-9m^3 Give each of your an swers in st andard

At a c onstant t emperature, the volume of a gas is inversely proportional to its pressure. 2.8times 10^6 Pascals and a volume of 1.7times 10^-8m^3 a) What will the volume of the gas be when it s pressure is 6.4times 10^4 Pasc als ? b) Work out the pre ssure of the gas when its volume is 8.7times 10^-9m^3 Give each of your an swers in st andard

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NigelMaster · Tutor for 5 years

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a) The volume of the gas when its pressure is \( 6.4 \times 10^{4} \) Pascals is \( 7.44 \times 10^{-7} \) m\(^3\).<br /><br />b) The pressure of the gas when its volume is \(8.7 \times 10^{-9} \) m\(^3\) is \( 5.47 \times 10^{6} \) Pascals.

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## Step1: <br />The problem states that the volume of a gas is inversely proportional to its pressure at a constant temperature. This relationship can be expressed as \(V \times P = k \), where \( k \) is a constant.<br /><br />## Step2: <br />We first use the given data to determine the value of \( k \). Given that the pressure \( P = 2.8 \times 10^{6} \) Pascals and the volume \( V = 1.7 \times 10^{-8} \) m\(^3\), we can substitute these values into the formula to find \(k \).<br /><br />### \( k = V \times P = 1.7 \times 10^{-8} \times 2.8 \times 10^{6} = 4.76 \times 10^{-2} \)<br /><br />## Step3: <br />a) To find the volume of the gas when the pressure is \( 6.4 \times 10^{4} \) Pascals, we rearrange the formula to \( V = \frac{k}{P} \) and substitute the values of \( k \) and \( P \) into the formula.<br /><br />### \( V = \frac{4.76 \times 10^{-2}}{6.4 \times 10^{4}} = 7.44 \times 10^{-7} \) m\(^3\)<br /><br />b) To find the pressure of the gas when its volume is \(8.7 \times 10^{-9} \) m\(^3\), we rearrange the formula to \(P = \frac{k}{V} \) and substitute the values of \( k \) and \( V \) into the formula.<br /><br />### \( P = \frac{4.76 \times 10^{-2}}{8.7 \times 10^{-9}} = 5.47 \times 10^{6} \) Pascals
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