If #12 L# of a gas at room temperature exerts a pressure of #9 kPa# on its container, what pressure will the gas exert if the container's volume changes to #3 L#?
The pressure is
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Using the ideal gas law equation ( PV = nRT ), where ( P ) is pressure, ( V ) is volume, ( n ) is the number of moles of gas, ( R ) is the gas constant, and ( T ) is temperature, and assuming the number of moles and temperature remain constant, we can use the formula ( P_1V_1 = P_2V_2 ) to find the new pressure. Given that the initial volume is 12 L and the initial pressure is 9 kPa, and the final volume is 3 L, we can rearrange the formula to solve for the final pressure: ( P_2 = \frac{P_1V_1}{V_2} ).
Plugging in the values, we get ( P_2 = \frac{(9 , \text{kPa})(12 , \text{L})}{3 , \text{L}} = 36 , \text{kPa} ). Therefore, the gas will exert a pressure of 36 kPa when the container's volume changes to 3 L.
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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
- The gas inside of a container exerts #15 Pa# of pressure and is at a temperature of #450 ^o K#. If the pressure in the container changes to #16 Pa# with no change in the container's volume, what is the new temperature of the gas?
- A container with a volume of #8 L# contains a gas with a temperature of #370^o C#. If the temperature of the gas changes to #890 ^o K# without any change in pressure, what must the container's new volume be?
- The gas inside of a container exerts #12 Pa# of pressure and is at a temperature of #85 ^o K#. If the temperature of the gas changes to #17 ^oK# with no change in the container's volume, what is the new pressure of the gas?
- A container has a volume of #1 L# and holds #16 mol# of gas. If the container is expanded such that its new volume is #5 L#, how many moles of gas must be injected into the container to maintain a constant temperature and pressure?
- The gas inside of a container exerts #15 Pa# of pressure and is at a temperature of #60 ^o K#. If the pressure in the container changes to #36 Pa# with no change in the container's volume, what is the new temperature of the gas?

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