How many moles of oxygen gas occupy 675 mL at if the oxygen gas was collected over
water at 843 mmHg ?
(Vapor pressure of water at )

Ask by Harper Bradley. in the United States

Nov 22,2024

Question

How many moles of oxygen gas occupy 675 mL at if the oxygen gas was collected over
water at 843 mmHg ?
(Vapor pressure of water at )

Ask by Harper Bradley. in the United States

Nov 22,2024

UpStudy AI · Accepted Answer

To solve this problem, we need to use the ideal gas law to find the number of moles of oxygen gas. The ideal gas law is given by:

$$ PV = nRT $$

where:
- $$ P $$ is the pressure of the gas,
- $$ V $$ is the volume of the gas,
- $$ n $$ is the number of moles of the gas,
- $$ R $$ is the gas constant, and
- $$ T $$ is the temperature of the gas in Kelvin.

Given:
- Volume of oxygen gas ($$ V $$) = 675 mL = 0.675 L (converting mL to L),
- Temperature ($$ T $$) = $$ 29^{\circ} \mathrm{C} $$ = 302 K (converting Celsius to Kelvin),
- Pressure of oxygen gas ($$ P $$) = 843 mmHg - 30.04 mmHg (vapor pressure of water) = 812.96 mmHg = 108.13 kPa (converting mmHg to kPa).

We need to find the number of moles of oxygen gas ($$ n $$).

First, let's convert the pressure from mmHg to kPa:
$$ P = 843 \, \text{mmHg} - 30.04 \, \text{mmHg} = 812.96 \, \text{mmHg} $$
$$ P = 812.96 \, \text{mmHg} \times \frac{1 \, \text{kPa}}{7.5 \, \text{mmHg}} = 108.13 \, \text{kPa} $$

Now, we can use the ideal gas law to find the number of moles of oxygen gas:
$$ n = \frac{PV}{RT} $$

Substitute the given values into the equation:
$$ n = \frac{108.13 \, \text{kPa} \times 0.675 \, \text{L}}{8.314 \, \text{J/mol*K} \times 302 \, \text{K}} $$

Calculate the number of moles of oxygen gas.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{108.13\times 0.675}{\left(8.314\times 302\right)}$$
- step1: Remove the parentheses:
  $$\frac{108.13\times 0.675}{8.314\times 302}$$
- step2: Multiply the numbers:
  $$\frac{72.98775}{8.314\times 302}$$
- step3: Multiply the numbers:
  $$\frac{72.98775}{2510.828}$$
- step4: Convert the expressions:
  $$\frac{\frac{291951}{4000}}{\frac{627707}{250}}$$
- step5: Multiply by the reciprocal:
  $$\frac{291951}{4000}\times \frac{250}{627707}$$
- step6: Reduce the numbers:
  $$\frac{291951}{16}\times \frac{1}{627707}$$
- step7: Multiply the fractions:
  $$\frac{291951}{16\times 627707}$$
- step8: Multiply:
  $$\frac{291951}{10043312}$$
The number of moles of oxygen gas that occupy 675 mL at $$ 29^{\circ} \mathrm{C} $$ if the oxygen gas was collected over water at 843 mmHg is approximately 0.029069 moles.
The number of moles of oxygen gas is approximately 0.029069 moles.

How many moles of oxygen gas occupy 675 mL at if the oxygen gas was collected over
water at 843 mmHg ?
(Vapor pressure of water at )

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How many moles of oxygen gas occupy 675 mL at if the oxygen gas was collected over water at 843 mmHg ? (Vapor pressure of water at )

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How many moles of oxygen gas occupy 675 mL at if the oxygen gas was collected over
water at 843 mmHg ?
(Vapor pressure of water at )