If gas at 25.0 °C occupies 360 liters at a pressure of 100 kPa, what will be its volume at a pressure of 2.5O kPa?

Question

Wyatt Atkins · Accepted Answer

14,400 L

Use the formula #(P_1V_1)/(T_1) = (P_2V_2)/(T_2)# (where T is the temperature in Kelvin, V is the volume, and P is pressure) 1. Enter the calculated values in the formula. Remember to multiply 25.0 °C by 273 to get 298 K (273 + 25). #(100 * 360)/298# = #(2.5 * x)/298# 2. Since the temperature doesn't change, the 298 K can be removed from the equation! #(100 * 360)/cancel(298)# = #(2.5 * x)/cancel(298)# 3. Determine x. #36000 = 2.5x# #14400 = x# The total you answered was 14,400 L.

Olivia Anton · Answer

undefined To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional when the temperature and amount of gas are constant.

Using the formula for Boyle's Law: $P_1V_1 = P_2V_2$

Given:
$P_1 = 100 \, \text{kPa}$ (initial pressure)
$V_1 = 360 \, \text{L}$ (initial volume)
$P_2 = 250 \, \text{kPa}$ (final pressure, converted from 2.5O kPa)
$V_2$ (final volume, what we want to find)

Plugging in the values:

$100 \, \text{kPa} \times 360 \, \text{L} = 250 \, \text{kPa} \times V_2$

Solving for $V_2$:

$V_2 = \frac{100 \, \text{kPa} \times 360 \, \text{L}}{250 \, \text{kPa}}$

$V_2 = \frac{36,000}{250}$

$V_2 = 144 \, \text{L}$

Therefore, the volume of the gas at a pressure of 250 kPa will be 144 liters.