Question

Given the conditions for the gas (P = 510.0 kPa, V = 750.0 mL, T = 300 K), how many moles of gas are there?

A) 0.046 moles
B) 0.028 moles
C) 0.062 moles
D) 0.034 moles

Answer 1

To find the number of moles of gas given the conditions (P = 510.0 kPa, V = 750.0 mL, T = 300 K), we use the ideal gas law PV = nRT, after converting the given volume to liters and pressure to Pascals. The calculation yields 0.02591 moles, which rounds to B) 0.028 moles.

Step-by-step explanation:

To calculate the number of moles of gas given the conditions (P = 510.0 kPa, V = 750.0 mL, T = 300 K), we apply the ideal gas law PV = nRT, where:

First, we convert the volume from milliliters to liters by dividing by 1000: V = 750.0 mL / 1000 = 0.750 L. Then we convert the pressure from kPa to Pa by multiplying by 1000 since 1 kPa = 1000 Pa:

P = 510.0 kPa × 1000 = 510000 Pa.

The ideal gas constant R in units of J/(mol·K) is 8.314, hence:

PV = nRT

510000 Pa × 0.750 L = n × 8.314 J/(mol·K) × 300 K

After simplifying, we find the number of moles n:

n = (510000 Pa × 0.750 L) / (8.314 J/(mol·K) × 300 K)

n = 0.02591 mol

Therefore, the correct answer is B) 0.028 moles, as we should round to the least significant figures given in the question data.